There's another angle to this: the schools are making money off the performance of the players. By that I mean that the rep of the school is enhanced and it gets more contributions; the ticket receipts help, but aren't the main thing. Given that the players are told that they can get an education in exchange for athletic performance, the 4 year commitment is implicit in the contract. The kind of processing yeti is talking about is now the main argument for recognizing that college athletes are employees of the school, allowing them to move freely between schools, and allowing the formation of unions of players. If the athlete isn't going to get a full ride from the school for the course of his education, why not recognize facts (something a lot of people here call for then studiously avoid) and change the teams to semi-professional status? Sure, that would mean the end of major college football, but everything else would be on the up-and-up.
Now that really is the choice. You give the young men a full scholarship for their entire time at college or you treat them as employees. The analogy to regular academic scholarship fails since the schools aren't profiting from the performance of those students; indeed, they are a substantial cost. Demanding academic performance to keep a scholarship makes perfect sense, given that. But athletic scholarships are given in the hope of earning considerable support and additional funds from athletes's performance. There's a quid pro quo there that should to be recognized. It's the failure to do that that characterizes "Big Boy Football" and it will - and not in too short a time either - destroy college athletics to the detriment of both schools and players.