Why would I use an electric bike?

I'm healthy for my age. When I ride, I want to be burning all the calories I can. My commute is only 3-4 km. Why would I want an e-bike?

You probably wouldn't. E-bikes are for helping you go farther or faster^* than you could on your own. Since you don't seem to need that, an e-bike doesn't seem to have any advantage for you.

^* In most countries, e-bikes have to cut out the assistance at around 25km/h (16mph) so "faster" only applies if you're cyling slower than that.

I don't have an e-bike. But some acquantances do or do/did think about getting one:

• One lives in a flat region as well, and tries to convert from car-driving to work to e-biking. Emphasis is on not arriving sweaty (possibility to change, but not to shower), but still in a reasonable time.
  So, no reason for you.

• One other acquantance who was thinking about an e-bike lives in a hilly region with the "flattest" possibility to get to work being 150 m elevation gain (half of that in a steep ascend just before arriving) and 225 m elevation gain on the way back.
  I do see far more e-bikes in hilly regions. Again, no reason for you.

• I've been living with 150 m difference in elevation from work for a couple of years, but fortunately that was almost exclusively down in the morning and up on the way home. The thought of an e-bike was somewhat tempting, but not that much: if I didn't feel like the 20 % incline on the usual way, there was another (longer) way that didn't require that much residual will power after long working days (or a party).

• I've heard as an argument for e-bike: in urban settings, bikers (just as everyone else) have to stop frequently, and get going again. This acceleration is the annoying and power-consuming part of biking in cities (particularly if you carry kids and possibly groceries around). An e-bike may help with that.
  Don't know whether that could be a reason for you, probably not, though, if your emphasis is on maximising your energy output.

I had an e-bike conversion - it was a replacement front wheel with a hub motor, and a battery pack in the main triangle.

After a year I sold the kit on - the bike was simply too fast, and I wasn't getting the exercise. Plus I was smashing through strava KOMs which wasn't really fair to those who worked hard.

Another negative for that conversion was that a fat rider on an old 90s steel MTB shouldn't be going 45 km/h, and cars would routinely pull out in front of me, or open car doors. Also, the bike's cantilever brakes were not really specified or rated for hauling down 30 kilos of bike plus a hundred kilos of rider and whatever I was moving. Brake pads lasted a couple of months tops.

The final straw was general traction. On any slightly damp day I got wheel spin when accelerating - the pedal action unweighted the front wheel and made it loose traction. The bike was incredibly keen to slip sideways, especially if I came into a turn or corner a bit fast (which was often) And while I never fell or had a collision, there were multiple times I took a corner too fast and ended up on the wrong side of the road. Some of that was doubtless my... enthusiasm for going fast, which could have been unlearned.

So an ebike makes riding easier and less work, which is less exercise overall. For me, riding faster than others was the attraction, but it wore off over time and now I ride a road bike and a recumbent bike faster and further than that electrified one.

Question really becomes - why do you ride ?

Each of the responses to your question addresses the OP's particular situation and concerns, i.e., recreation and fitness. However, someone discovering this question is probably asking themselves "Why should I?", so I'll try to speak to them. In short, you should use an electric bike to get a carectomy.

The now-defunct website carectomy.com introduced me years ago to this concept: the painful but ultimately satisfying process of extracting cars from people.

E-bikes were key to getting my carectomy. My e-bike helped me, as a car-bound commuter, evaluate the time/money/carbon footprint tradeoff on investment, all in order to play a trick on myself. I purchased nice saddlebags, rain gear, and a nice bike to put myself in a position where I could make no excuses about biking to work. On warm, sunny days, riding instead of driving was easy. On rainy days, it was less easy but tolerable with gear. On frigid days, the combined cost of the gear and bike, as well as not having a car to fall back on, forced me to bike anyway. All this makes trips to the store etc. trivial when compared to a commute, and suddenly, my carectomy is complete.

Folks browsing Stack Exchange Bicycles often ride for health, sport, and similar reasons, evaluating technique and gear choices, for example. Yet the true target market of e-bikes isn't bikers, it's people who need a carectomy. If the question is "Why would I use an electric bike?", I offer that you would use it as a lever to change your behavior and get that carectomy you always needed.

I live in an extremely flat city that lies about 15m above sea level. One has to drive an hour or two to reach even rolling hills.

Several decades ago, I rode quite a bit, and accumulated a decent "sport touring" road bike, a mountain bike, and a track bike. Then I stopped riding for a couple decades.

Now I have returned to riding casually and found BSE, and it's full of questions about electric bikes, which didn't exist when I was riding before.

I'm healthy for my age. When I ride, I want to be burning all the calories I can. My commute is only 3-4 km. Why would I want an e-bike? What advantages do they offer?

There is practically no advantage for a 3-4 km commute in a non-hilly region.

I have found that the most benefit electric bike offers is that:

• It helps tremendously when going up hills
• It helps when starting from traffic lights -- if there are a lot of traffic lights in your non-hilly city, you could perhaps benefit from an electric bike but otherwise don't
• It helps you after you become tired, so longer distances are feasible, but of course then the battery life starts to be eaten rapidly
• It allows you to always use a high gear even though you might need to occasionally start moving at a slight incline

My electric road bike helps me only when starting from traffic lights and going up hills. It normally does not help in flat terrain because the 25 km/h limit of the electric assist is reached even with no electric assist. However when I become really tired, then the e-bike starts to help also in a flat terrain.

I stopped riding for 5 years and now I resumed riding with two e-bikes, an e-fatbike and an e-roadbike. I'm not completely healthy for my age as I'm somewhat overweight, which is quite annoying when going up hills. An e-bike helps in that.

Don't buy an e-bike unless your commute is full of traffic lights. Or, if there are reasonably many traffic lights with slight incline after them, and you absolutely hate gear changes, then you could also benefit from an e-bike allowing you to avoid those gear changes.