Schools are not for profit sports teams. All the sports leagurs also have some antitrust exemption. Again, how can you have a contract that limits what school a person can attend? You cannot. Another problem is that players are not exactly employees of the university, but rather this quasi student/employee. The employment non compete contract fails because academics are still involved. They would have to be full time employees with no other status with the university to make that contract work.
Also, since the players are getting their money from third parties outside the school, any contract that limits the players ability to make money from third parties woulld be illegal.
This is out of the NCAA and the schools' control until they are granted some exemption to limit transfers.