I think you're probably right that visualization doesn't work very well if used alone, and doesn't work as well as executing the movements themselves, but there are a lot of situations where it makes sense to visualize something instead of actually doing it–and this seems to at least help.

For example, recently I had to teach myself the poomsae (taekwondo equivalent of kata) for my next belt testing by watching Youtube videos the night before. It obviously didn't work for me to stand in front of the computer screen and do all of the movements–any move that took me sideways or backwards would result in me no longer being able to see the screen, and thus not knowing my next move. So I sat in a chair and visualized as hard as I could as I watched, making small movements with my hands and feet to represent kicks and punches, but imagining myself doing the whole movement. After 5 or 6 repetitions, I was able to stand up and go through the whole sequence in my living room, using my whole body.

Likely this worked because I already knew a whole bunch of basic moves, which were included in the poomsae, and just had to string them together in a new order, with transitions in between. (And even for the transitions, I've probably done almost every transition from one move to another at least once before 'in real life.')

I think a lot of athletes use visualization because, well, it's not practical (or even possible) to train all the time. Your muscles have limits. Even if you don't reach those limits, the training time booked on the rink or in the pool or whatever is limited. So you get the most out of it that you can, and then you take advance of "downtime", which would otherwise be useless to training (i.e. sitting on public transit on the way home) to visualize. I don't know if anyone'd done a study of this, but for athletes who are already training a lot, I expect doing some extra visualization on top of it helps.