If you had to wait for all pedestrians to be out of the crosswalk, there's plenty of places where turning would be essentially impossible -- and there's an argument to be made that anywhere with that much foot traffic ought to be turned into a pedestrian-only zone, well, right now there are both cars and pedestrians and requiring the crosswalk be clear before going would make things even worse.
NY prohibits driving in the occupied half of a crosswalk. i.e. from center line to the curb. This is almost impossible to obey in NYC with heavy ped flows but it is a sensible way to combat drivers clipping you from behind.
