Of course colleges have rights and naturally there would be restrictions, but I would think it would be better for the college ( in behalf of all of its sports - major and minor) to negotiate those rights instead of start paying athletes.
Guess it comes down to a cost analysis basis for the college.
No need to negotiate rights. This is our school’s policy. You are on scholarship. We are paying for you to be here. Do you want to be here? Yes or No?
End of discussion.