How changing tennis balls influence players using serve and volley?

I haven't heard much of anything about the balls being faster - but there are definitely other factors that have contributed to serve and volley (S&V) becoming a much less common playing style in tennis these days. The balls used across ATP tournaments are generally the same (Head ATP is the official ball brand of the mens tour currently), with the exception of the brand used at Wimbledon - I think Wimbledon uses a Slazenger grass-specific ball that has a little bit more bounce to it since the grass at Wimbledon provides the least amount of bounce compared to clay and hard court surfaces.

As far as what has contributed to the decline of S&V style tennis - there are several factors but there is one that stands out above the rest and is sort of the cause of the other factors.

It's the strings.

Advances in string technology (mainly polyester strings) have made it so that players can take a bigger, harder swing at the ball and at the same time generate more topspin so that the ball stays in the court.

Also, tennis players - physically speaking - have followed the trend seen in other sports and are now generally taller, stronger and faster on average than the players seen in prior decades (70's/80's/90's).

Grass court tennis (what little of it is played each year) actually used to be considered the fastest surface of all and saw a lot of "boring" matches played where the number of aces and service winners hit was much higher than on other surfaces. To try and make grass court tennis a little more interesting, over the past decade or so (at Wimbledon) they have added a little bit of sand to the ground beneath the grass in order to slow the grass game down just a little bit.

So taking all of these factors into consideration together (the strings, player physicality and surface changes) - it means that a tennis player in today's game trying to execute a serve & volley style game has to face faster returns with more topspin on the ball, and an opponent that can run down more of your volleys than in prior decades and a surface that is giving S&V tennis less of an advantage than it used to.

In the end, serve & volley tennis just isn't seen as being as effective as baseline tennis from a numbers & percentages standpoint - and tennis is all about the percentages. The margin between winners and losers at the top of the game is very thin and plenty of matches are won by just a couple of points here and there going one player's way.

Since serve & volley isn't seen as being as effective, this also means that fewer players want to develop a game around it and fewer coaches try to teach it to junior players. This effect just kind of implodes inward on itself and now you have a style of game that very rarely includes serve & volley tennis.