Hmm that's an interesting point of view. I suppose my answer to that would be that I don't see the analogue with Taylor Swift, exactly, since she established herself independently of the institution. That's not the same since football players receive a great deal of free publicity from their participation in athletics, and so the University can be attributed the rights (or most of the rights) to the profit from that publicity. This is especially true since almost no football player is nationally-known prior to being associated with a national university. Even great football players from lesser-known universities have very little national recognition most of the time because fame is primarily derived not from their ability as individuals, but from the name and logo on their uniforms.
I prefer the analogy that says that the athletes are like product developers at a major company----I'm going to use the example of a designer at Apple. A designer might sign on to Apple for $60k a year. He creates the design for a product that eventually becomes 20% of the revenue stream for Apple, a multi-billion dollar company, and his name is on the design patent. His product is worth literally billions (or at least hundreds of millions) of dollars! Shouldn't he get a share of the profits? After all, without him, there is no product. No one else could come up with exactly the same design for an iTurd, and that design has been praised by iSh*t lovers everywhere. His subtleness, his attention to detail, his incredible sync with customer needs----it's a masterpiece, truly, and the media world has recognized that so much that his name alone adds value to future products. Shouldn't Apple pay him more than the $60k a year he agreed to when he signed on to the company, so he can share in the profits his work earns for Apple?
Of course not. He was only able to find success because of the incredible reputation of Apple, because of the world-class marketing team, the Triple-A rated support of the Moron Bar, and the customer's unending faith that any iCrap squeezed out by Apple is worth a fortune. And if he had been designed an unsuccessful product, he would still be owed his salary---all the risk was taken up by Apple, who also took upon the responsibility of manufacturing, shipping, and sales, without which the design, unpatented because no one would otherwise pay a ridiculous sum to get it patented, would languish unused in a cabinet somewhere.
Of course, it's a free market and our theoretical designer has the freedom to withdraw from Apple at any time and start his own company, so he can profit in scale with his success. But he finds that he never appreciated the sheer amount of work that went on besides his product design to create something that people wanted to buy---and without the Apple name backing him, his iSh*t is just perceived as regular sh*t, and sales don't go well.
Athletes receive an education, room and board, and various per diems, gifts, equipment, and other benefits worth more than $60k a year, and the fact that this isn't in cash is irrelevant---it's a compensation package they agree to when they sign up, and they are, of course, perfectly free to not sign up and instead choose another option, like acting as a regular student. If they were a regular student, they could be free to utilize their athletic talents as they see fit without the gravity of NCAA rules holding them back. They could take on the time and effort of organizing a team that people want to watch, of branding it and selling it and using their theoretical accounting degree, for which they are paying full price, to make financial statements for ticket sales and pay the taxes on these. They are free to do all this at any time, since no one is forcing them to play football for any university. That's really difficult, obviously, but entrepreneurs make this choice to give up the assurances of a big company to create a startup all the time, with all the risks and financial losses that entails, when they feel that their compensation or personal inputs to the enterprise or even the use of their name are not satisfactory.
Or football players can STFU, recognize that they are in a position of incredible success and envy among their peers, and that if they would like to trade places with someone who is $150+K in debt who works their part time job every moment they're not in the classroom or working on problem sets, they are perfectly free to do so, and no one will question them if they would like to sell their image themselves. Of course, they may find that such a route will not get them what they seek.