What are you talking about? You reference the "sport" several times... as if the NCAA supports a sport. The NCAA is composed overwhelmingly of small schools with small budgets, playing a wide variety of sports. 99% of NCAA institutions have small budgets, and coaches that are solidly middle class, and athletes that will never play anything professionally.
If the sport you are talking about is college football, then the NCAA itself makes little money off CFB. Most of those dollars are managed and received by the conferences (or the individual institutions, obviously).
Citing that "the NCAA" itself makes very little money from college football is a disingenuous direction of argument, because as I stated previously, and as you partially acknowledged, the enormous amount of money in college athletics that comes from college football goes into the hands of the representative institutions and individuals who receive it in other ways. It also phrases college football as if it is a tertiary concern for the NCAA, which couldn't be further from the truth. Rule changes impact every member of a nearly $4 billion per year industry and infraction committee actions change financial positions of individual institutions and even whole conferences to the tune of millions of dollars. Every single year. There is tremendous pressure on the NCAA from college football specifically, considering the constant controversy over football recruiting infractions, or lawsuits over this or very similar issues, far outweighing the pressure on it from even the next plausible competitor in basketball. There are more NCAA athletes playing college football than the next three largest collegiate sports combined, and athletic spending at NCAA institutions is weighted towards college football with an insane ratio.
I cite "a" sport, because there is only really one sport paying the huge athletic bills at the most prominent NCAA institutions across the country, and it ain't volleyball. Coincidentally, there's only one sport across the country where a tertiary player on a second tier team could earn a profit by leveraging his likeness indirectly, which is seeing individual players directly subjected to NCAA ultimatums against that activity to prevent the practice from becoming more wide spread; it certainly isn't track and field. A discussion of NCAA behavior with regards to things like "profit" is fundamentally a discussion of college football, for all intents and purposes, and just because there are hangers on in lacrosse and soccer and a myriad other things doesn't succeed in diminishing that. College football is the biggest issue on the docket of the vast majority of interested parties who compose the NCAA, even at the smaller schools with the wide variety of sports; and let's not pretend as though the smaller schools have anything approaching the level of influence in the organization that is wielded by the larger ones.
At the end of the day, the NCAA writes the rules for the sport and enforces them, and at the end of the day, the sport is what makes the athletic world revolve. A world where the NCAA is not principally concerned with the sport is completely imaginary. A world where the member institutions don't act in their own athletic interests, which are dominated by football revenues and expenses, is completely imaginary. The NCAA is not deserving of its non-profit status, it is a cartel whose actual function is enforce "amateurism" on the portion of the sport which forms the basis of the value that is reaped in revenues by the member institutions and their affiliates. This practice should be abolished, and there are plenty of laws on the books today that could be read, very reasonably, to accomplish that feat.
If you have some grander philosophical objection to the idea that people could do anything for less than purely self-interested reasons — after all, the head of the United Way makes a lot of money, and that first-grade teacher accepts money so she's basically prostituting herself, and nuns are just trying to earn their way to heaven, heck, aren't we all? — then we should be having a very different conversation. And you'd be proving why they call theology the 'queen of the sciences.'
Sure, people can do all sorts of things for reasons other than pure self interest. Those things don't generally beget billion dollar media empires that generate insane profits and support multi-million dollar salaries across the country. But hey, maybe this one's the exception and it's all just a big misunderstanding. It's easy to see, how, out of interest for someone other than myself, I could deprive someone of their ability to pursue their own interests while I gleefully pursue profit on the back of their efforts nonetheless. That wouldn't be self-interested behavior at all. Sounds like standard non-profit stuff to me!
