Why don't any USA professional leagues use promotion/relegation?

Lots of reasons.

First, and primarily, there are a lot of sports, and sports teams, competing for spectators' attention in the U.S., and the subsequent ad dollars for TV airtime, stadium naming rights, on-field logos, etc. I realize there are other sports besides soccer in Europe, but the gap in overall popularity between association football and basketball or handball in Europe is much wider than the one between the big three team sports in the U.S. There are also more teams in each top-tier sports league in the U.S. than in the English Premiere League (or anywhere else in UEFA), with 32 NFL teams, and 30 teams each in the NBA, NHL and MLB. More teams means more games means more airtime needed.

Second, and just as important, is risk/reward for the players. Gridiron football is a violent, dangerous sport, and to be picked in the NFL Draft says as much about your ability to avoid injury as it does for your skill. Despite this, ejections are relatively uncommon in gridiron football, so it's an exceptional case when a player is called to answer for causing injury to an opponent. The result is that, by the time a football player is drafted into the NFL, they may already be at the halfway point of their career in terms of the wear and tear on their bodies, which will stay with them the rest of their lives. There simply isn't enough reward inherent in playing the game at anything less then the premiere professional level to justify the risks the game presents.

Association football, in contrast, is technically a non-contact sport; aggressive actions made towards opposing players are penalized. As a result, injuries in soccer, though they do happen, tend to be more minor, and players who deliberately injure opponents are held to account for those actions more frequently. That allows soccer players to have careers spanning decades, rather than the average of about 10 years that you see for NFL players other than QBs and kickers. Now, this emphasis on injury being against the spirit of the game is seen in other U.S. sports, even hockey in more recent times, and you do see longer careers in those leagues, with basketball and baseball players continuing to dress for games into their 40s. However, the mentality of "move up or move aside" is still prevalent as players grow up through the school leagues; if you don't end up playing for the pros, there's not much money or opportunity continuing to play past your college years.

Which leads to the next reason; in the U.S., the player, not the team, is regarded as being mobile. The sports that do have notable minor leagues in the U.S., being baseball and hockey, typically have teams in various tiers that are either owned outright by one franchise or have partnership agreements. That's in addition to the prevalence of college sports teams in the U.S. (and by the by, if you want to see a loyal sports fan on the level of European soccer fans, don't look at the pros; look at college grads cheering their alma mater). The net result is that the player "grows up" through a series of teams, hopefully developing into a player that can compete in the premiere leagues, and the job of all the lower leagues is to help the player with that development, then let him go. In Europe, it's not just the player but the team that is mobile in the overall structure of the league. They player still grows, still develops, but the team that helped him do that is much more willing to try to hang on to him if they can, because this star striker or forward midfielder could be the ticket to a league championship and promotion.

We still haven't gotten exactly to why the U.S. hasn't bought into that same mentality, though, and the next reason is the one I think is most important; geographical coverage. The U.S, without Alaska (no professional sports teams in that state to speak of), is about the same size as all of non-Nordic Europe combined. That means that maintaining a national fan base for a sports league in the U.S. requires paying very careful attention to the geographic dispersal of your teams. In England, you'll notice the EPL teams are concentrated in the London metro and the Manchester/Merseyside area, with Birmingham growing up as a third center for English football. That's mainly happened through promotion and relegation; teams in urban centers have more spectators, get more ticket and ad revenues, can afford to hire better players, and become better teams, moving up into the premiere league and forcing out the teams from outlying areas.

Now, that's OK in a country with a total land size about the same as that of the U.S. Eastern Seaboard; if you want to cheer on a premiere-league team, there's one within a couple hours of pretty much any town in England. Or, as the commenter states, you can keep cheering for your hometown team even if they're not in the premiere league.

In the U.S., however, that kind of league management would result in a disproportionate number of teams being crammed into the East Coast cities, much as the EPL's teams have gravitated to London and Manchester/Merseyside. That would place a lot of large "heartland" cities, each with populations in the millions, at least a day or more away from the nearest professional team by car. With no minor leagues to speak of due to the risk-reward problems of many of these sports, support for the sport in any form in areas without a major team would simply die out, robbing the leagues of valuable TV time. That would be compounded by the concentration of teams in the most populous areas, which force teams to fight each other for the biggest slice of the revenue pie. As a result, teams are carefully managed by franchise owners and league leadership to ensure that the teams are spread as evenly as can be supported around the populous areas of the U.S., giving each team a built-in home crowd.

That, in turn, requires the teams to be kept on roughly equal footing; it's in the league's best interest to keep all of the teams it has financially healthy and competitive, and the two go hand in hand. So, instead of punishing franchises that can't buy a good team, we give the worst teams the first picks of new incoming talent. Instead of letting the richest teams self-perpetuate by spending more money on talent than anyone else can, we put salary caps in place to ensure no team can spend more than any other on their players. The current scheduling system even gives each team a game against a team from another conference they normally wouldn't play, with the same division ranking as their own, meaning the better teams have overall tougher opponents. This egalitarian approach lets dynasties rise and fall over a period of a few years each instead of a few decades (as is seen in baseball and in collegiate sports, where the school's reputation as a sports powerhouse is self-perpetuating over long timespans), and gives every franchise and every fan the best chance for their team's success.

The United States does use a relegation model, but it is the struggling player(s) who gets relegated to a team in the minor leagues, rather than relegating the entire team. It has the same effect of ensuring that only the best play in the top league; the system is just organized differently.

There are many reasons it is done this way, but the most obvious is that the talent gap between, say, and NBA team and a Developmental League team, is huge. No D-League squad could come close to competing with even the worst NBA team. Asking them to would not make much sense, and no one would go to see the games because they would be completely one-sided.

In the light of the existing answers, and the wikipedia link given in the first comment to the OP, I believe the only factual answer one can give is: the difference in the business model.

The franchise system, used in the Northern American leagues, both for the league itself and the teams, aim to secure and maximise the interest and viewership for the sport in question. It is partially because the sport itself is birthed as a business with an interest in profit.

Many sports associations in Europe, starting presumably with football, is formed based on organised competition. The goal is not to maximise viewership or profits, but rather sportive success both in athleticism and management. I guess one could also argue that in Europe the common idea is that the club belongs to the fans and tradition, rather than he/she who pays the most. Admittedly, larger leagues have become huge franchises based on TV-sales, but it is still unthinkable to see establish clubs move or change their profile (i.e. color, logo etc). It is simply unthinkable that Steven Gerard playing for any other club, or Liverpool FC would, for instance move to London or anywhere actually. This is a common recurring event in the franchise model, where teams move around the nation (here's a parody of franchise relocations from Baseketball the movie).

All in all, relegation/promotion model aims to optimise the sportive success rather than viewership and tv-profits. I hope that answers your question

Not sure I buy the geographic answer. Russia and Brazil are physically huge countries with horrible infrastructures for getting around that run league systems. And yes, the top tier teams do concentrate in the larger cities. But this is true of the US teams as well, simply because large populations and major TV markets do go together.

One of the vested interests not referenced is wiping out the draft lottery system. If teams with poor seasons do not get top draft picks, they would stay poor teams and be relegated to the next tier. Yes, this is hard on teams with long losing traditions, but if you live in "the cellar", shouldn't you be competing in a more appropriate weight class?

Another thing that would go is the way franchise owners can move teams without consulting the fans which has sparked several notable outrages (Brooklyn Dodgers, Baltimore Colts, Cleveland Browns). This almost never happens in league systems as fan bases effectively own the teams.

Sport around the world is about success on the field and the fans, in the US it is a franchise to make money. The owners of a team like the Mets for instance would rather come last every year in the 'Majors' and have the season over before half the games are played, than play in the 'second division' at the top of the league, simply because they would make more money from TV coverage in the 'Majors'. It isn't in the American mind to be second best, even when (as with many teams) you clearly are second best, and have to play teams many times better than you all season. In the US it's about the money the franchise can bring, in the rest of the world it is about being as good as you can be, whether that is PL Champions or 4th tier runners up.

One aspect that has been ignored in this discussion is the origin of the competition. In Europe all teams started locally as amateur teams. When you play, you have a vested interest in playing at a suitable level. Some amateur teams are only competing for the love of the sport, others are trying to be as good as they can within the limits of being an amateur. This has led to the diversification to different playing levels aka divisions with the possibility of promotion/relegation when teams are getting worse or better on the field.

Most professional clubs are the top of the pyramid of an organisation with teams at various levels of competition, with only the top as professional and the teams below as amateurs, extending to youth level. It just happens to be that in England professionalism has led to a system with multiple levels of competition. In other countries there are only 2 or 3 levels of professional football competition. Look below that level and you will find amateur football/handball/hockey, etc.

In the USA this environment of establishing local 'grass roots' teams never took off, as the only organised play (football, baseball, etc) was through school. There was no need or requirement for organised sports on amateur level, since it was provided through high school, followed by university. After that, the real world awaits and there is no time, no need, no opportunity for spending so much time on recreational organised sports.

The answer is simple. It's all about money! The franchise model used in the states is all about profit above everything else. In Europe it's about sporting prowess, history, passion and belief. Belief that your local club can work it's way up and play with the big boys.

A point in case is Wimbledon FC, who were a "non league club". Which basically means they were originally an amateur club. Within 5 seasons they worked themselves into the English Premiership, even getting to, and winning the FA Cup Final. That was every fan's dream. Ok within 10 years they had gone bust, were taken over, with the new owners proposing to move the club to the "new town" of Milton Keynes 40 miles away, where there was no existing pro soccer team and a readymade market of 400k people. The original fans, were having none of it, and started a new club AFC Wimbledon who were forced to start at the bottom of the pyramid. But through a desire and passion they have worked there team back up to our pro leagues and are in the same division as the now renamed MK Dons. That, I thought was the American Dream.

The jeopardy of promotion and relegation is where most of the excitement comes from in European sport and is what you are missing out most. You just can't see the wood for the trees. My own team are Watford FC, you follow them through thick and thin and believe me, there are more downs than ups, but the ups are all the more sweeter for it.

Just recently the American owned teams in the UK, Arsenal, Liverpool and Manchester United were instrumental in trying to start a new "Super League" for the biggest clubs in Europe with the sole intention of controlling the money to the detriment of the sport and not allowing their teams to be relegated from it. Thankfully, through popular support from fans, ex players, and even politicians the game as we know it has been saved. Long live promotion and relegation and all the passion that goes with it.