You will get more sit outs. Again, even choosing 4 teams show how difficult it is to get good, even matches. I would be more radical. Start a trade school for athletes. Rudimentary liberal studies...12th grade apc level...a profitable trade...and pro level sports development environment. These players could play against other schools or even pro teams and still go to school.
The educational hypocrisy of the so called major schools is too obvious.
Heck, I would limit it to basic finances, econ 101 and basic investing. If these guys get their dream they need the ability to have some money after they retire. Most of them get ripped off by their agents & business agents.