You’re right about top colleges succeeding largely because they can attract top students. That is their social and sorting value.
But at the high school level, these exam schools are the only way young scholars can receive a rigorous education. Taking away the objective, merit-based screening for admission would require the classes to be watered down just as they are in the rest of the NYC public school system.
I understand your point, but that's just not true. As many homeschooled kids demonstrate quite conclusively.