Somebody needs to explain to me how paying players would solve this problem. I suppose if you are paying them huge contracts, basically NBA level, it works but if you are paying something less or comparable to d-league wages (max +/- 26000, lowest $19500) and you get offered $150000 to go to University 6 you still take it. The second problem you have is that in deciding to pay players you have for all intents and purposes created a smallish minor league of teams that can afford to pay. Maybe 60-70. So you've ended the NCAA tournament because the MAAC champ ain't playing a pro team and it isn't paying its guys either. You also have title IX issues. Since you can't treat women differently you need to pay the women's team and if you pay football you need to pay 85-100 women too. What is the going rate for Women's rowing? It has been clear for ages now that revenues don't figure into the equation when it comes to Title IX implications. Some good ol' boys tried that 20 years ago arguing that football deserved more scholarships because it generated more revenues than women's tennis and it was shot down hard.
There are a huge number of other issues but the bottom line is that paying players doesn't begin to address the problem of illegal payments.