Illegal? How? Other students get paid for their extracurricular activities.
Apply it to all sports. Not many people with money are going to pay players for womens sports.
Other issues being what? We are talking about a multi-billion dollar per year industry where the majority of the participants get paid a low salary (schollies).
The market would dictate the going rate for superstars. There would have to be a bunch of rules, but it's better than the current system where the football factories have boosters that pay for players behind the scenes.