The NCAA and schools make millions of dollars off these kids and the kids see none of it.
Correction; about 15 schools do. If major college sports take that next big step in the direction of professionalization, say goodbye to about every current FBS conference when half their members move to some alternate, psuedo-Ivy League system. I wouldn't be surprised to see the sport slowly wither and die because interest will drop to about zero when no one but Alabama et all plays at the highest level.
And it's not just about money; there is already opposition and ambivalence to the idea of "big time" college sports at every campus in this country. I guarantee you programs like Stanford will hit the breaks purely on principle.