The majority of NBA players do come from the biggest programs. But the fact that they come from those programs is not the reason they are drafted. In an average year 40-45 college players are drafted. The majority of those players were considered top recruits before they started college and a high number of them were already well known by NBA scouts.
Thus the top high school players go to the biggest programs. But the program doesn’t generally make a player more draftable. A large number of kids would be drafted if they didn’t even go to college.
Fultz and Simmons are obvious examples that being at a top program doesn’t really matter.