Of course the NCAA isn't free market, it's "non-profit"<quoted text>
Those scholarships don't cost the school much of anything. It's an extra chair in a classroom that's already there, being paid for by kids whose families ARE paying. It's an extra bed in a dorm that's being paid for by someone else. The scholarship is merely a way for the school to bind the player to the school and prevent them from leaving for another school.
And they're NOT free to leave anytime and join a pro draft. Just ask Maurice Clarett. The NCAA saw to that. NCAA athletics is anything but "free market capitalism."
Legally, every single college athletics program is a tax exempt charity, IE it can get tax deductible donations. Which are a none too small source of income for programs that believe it or not don't really make much money, if they make anything.