I think it's post-may 15 that most movement occurs. It's possible for some to occur before, if enough people with offers formally withdraw and there are now open spots in the class.
But what happens is that even if a person decides long before May 15, they may not actually withdraw from all other schools up until the last minute, as students often hold on to their 8 acceptances like trophies (i'm quoting a dean of admissions who said this). So I think you're right that most students pretty much decide by the end of April, and send that deposit in to their top choice, but it doesn't necessarily translate into them withdrawing other offers just yet.
In this scenario, it's risky for a school to start heavily dipping in the waitlist, even if they have a very good rough idea of what the class is looking like, as a lot can happen in the final days, and all deans fear the prospect of over-enrolling, since it really screws up rotations/class schedules.