I don't know what country you're from, but in the US many colleges and universities are absolutely private, for-profit institutions.
You might have a personal, ethical disagreement with that, but it doesn't change the reality of the situation.
In fact, I'll bet most of the major, well-known institutions you can think of--MIT, Princeton, Brown, NYU, etc--are private, and for-profit.
Also many universities are public and not for profit.... you know the main ones that actually have well known sports teams... not uh MIT.
As noted in this article:
https://www.forbes.com/sites/kristidosh/2017/06/12/the-bigge...
> At many universities I polled, the university and athletic department split licensing revenue 50/50. So, even if the sweatshirt sold in the bookstore is specifically branded for the football program, that money is divided between the university and athletics.
If you want a fully publicly funded system with no private dollars flowing in to support it, elect politicians who will make that happen.
Unfortunately, in the US, that's simply not the way the system works today.