The coaches were always hopping around like that, that's one of the reasons the new system needed to happen, imperfect though it remains.
The taxpayers (nor the students) aren't really paying for any of this stuff though. Penn State specifically isn't even a truly public institution. The new revenue-sharing model is money that only comes from athletics, and NIL money does not come from the schools at all. Even before all this football paid for itself at the big schools- and also paid for nearly every other sport. Severing football (and/or basketball) from the universities would only end up hurting all the other sports, though that might also be the case in the current system.
It's a ridiculous system, but there's not really anything about the way athletics messes with a university's mission that isn't also true of politicians, corporations and donors.