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.

They have. It works much as you hypothesize. The Cambridge Handbook of Expertise and Expert Performance had a couple of chapters on it if I recall.