NCAA sports are a billion dollar industry. The athletic departments at state flagship schools give money back to the academic side which helps out the poor taxpayer. By the logic you played out, which I admit is pretty good, I only see two options.
1. Free market: coaches and players can make as much money as they can within some reasonable and legal constraints.
2. Amateurism: players get their full ride scholarships and nothing more. Salary cap on coaches to curb cheating. Cap on athletic department budgets and total revenue to curb cheating. TV money is split evenly among all the participating institutions by sport and goes to the academic side.
#1 is where we're headed, there's no going back now. Any attempt to curb that will be taken to court and sued out of existence. Again, I think it's going to kill the various sports - not in the literal sense, but casually committed players will eventually lead to casually committed fans. I've said it elsewhere on VolNation but there's a huge difference between supporting students who are attending a school, and supporting employees doing a job. They aren't the same thing, not at all. One you support unwaveringly because of their commitment to your community and your school. The other is an employee, so, they better do their job -- or else. And people can say "well, #1 is a more honest approach." To which I would say okay, but that's not appropriate for a scholastic setting. Hence my statement about divorcing them from the college brands. You want it to be a professional thing? Then make it one, and get it away from the schools.
#2 is better philosophically for the sport, and more in the spirit of intercollegiate competition. I wouldn't be opposed to stipends or some sort of compensation for time, I think that is fine and in line with other jobs schools offer for students. But the TV money is the problem and it can't be changed. It used to be handled differently, up until Oklahoma sued the NCAA and won the right to make money off TV rights as it saw fit. The current Supreme Court is already hostile to the NCAA, so I doubt control of media rights can ever bring that back to the table. Coaching salary caps wouldn't be a bad idea but you'll never get the heavyweights to agree to it because they want to exercise their dominant financial position to achieve success. And really, even in that new world, the players would still be suing for a slice of whatever reduced money there was, leading to further cuts, so, sadly, it's just not anything anyone would tolerate.
And don't get me wrong, the schools are ABSOLUTELY to blame for much of this. They sold the games, the experience, and even US the fans, in exchange for lots of TV money. They showed a terrible lack of stewardship for the health of basketball and football. And now we are more or less, unwillingly, part of the product that ESPN packages up and sells to advertisers. "Look at all these fans we can put your ads in front of." That's the core of it. We, and the thing we all love, were packaged up and sold off to the highest bidder.
Also, as a footnote, while I think you're right about the two paths, most schools don't make money on any of this. I want to say less then two dozen athletic departments operate in the black. What will be interesting to see (well, "interesting") - is what happens when the football players form a CBA and sue the schools. I wonder how many sports colleges will have to cut once they lose a chunk of their media money to the football players? My guess is, a lot. Oh well. At least we can watch all of Tennessee's college teams on ESPN!
... well, except when they're on Flohoops ... or ESPN+ ... or the Big10 Network ... ... hey, wait a minute, this deal sucks.