Compensation can be anything with value, not just money. But as Finwad said, fine pay the players but let them pay the cost of tuition. I'll bet it equals out or they come out at a loss.
To me, this construct points out the ridiculousness of what college athletics has become.
College athletic teams are supposed to be composed of students attending a particular school who want to obtain an education and at the same time participate in an athletic extra-curricular activity. Same as other students participate in Greek life, music, drama or whatever. When they represent the school particularly well or in a fashion that creates value for the school, the school awards a scholarship. That is the currency that college students representing their university are paid in.
One of the big reasons that this disconnect exists now is that colleges have allowed athletics to become basically an entirely distinct enterprise from their primary enterprise which is education and research. Today they seek out the best basketball players rather than the students who are the best basketball players. They end up with great basketball players, but those great basketball players often have NO interest in obtaining a college degree. If they have no interest in an education, why are they at a college?? When that is the case those kids have little interest in being compensated in the currency of free tuition.
Seems to me there is one of two ways this could/should go, on a go forward.
1. Adopt rules and make changes that returns college athletics to what it was originally intended to be, a pursuit for students looking for extra curricular activities while they are pursuing an education. Send those that are primarily pursuing a path towards playing athletics professionally somewhere else, like a professional minor league.
or
2. Allow colleges to sponsor professional teams where the players are paid whatever the particular college's budget will support. The athletes will be employees of the universities with no requirement that they take courses and pursue a degree. Completely remove the lie of amateurism.
As a compromise, maybe you have both models. Pro Division and Amateur Division.
Once you go to a fully professional model I don't see how the great majority of schools truly compete. The big state schools and schools that are in the largest population centers are likely going to dominate because they are going to have the biggest fan bases and the best ability to supplement the money that is evenly distributed with additional money so that they can pay the best athletes greater salaries.