At New York and Washington, many of the platforms are not all that wide and are shared by a track on both sides. Imagine letting people congregate on the platform waiting for their departure when another trainload of people arrives on the other track. Now you have baggage carts trying to address the arriving train while the platform is doubly full of people. Oh, and don't say simply route the incoming train to another track - it's not that easy, especially in New York.
Suppose you had a platform full of people waiting for a departure, and the track changes. Why, you say, would that happen? Oh, let's see, equipment failures, switch failures, ..., any number of snafus.
You definitely do not want to move people to the platform/train until it's ready. Now you might try to improve making that happen earlier.
At other places, such as in Norfolk Southern territory, the railroad does not want anybody up on the platforms until it's time for their train. In that case I would guess that it's partly for their concern of being sued in case somebody gets hurt.
jb