Athletic departments as a whole aren't profitable because the ridiculous amounts of profits earned by basketball and football can't subsidize the losses incurred by supporting the other sports.
But really, I think the issue here is that you're arguing at cross purposes. There's a strong argument to be made that the whole idea of the state running a profit-making sports team through its universities is flawed and borderline immoral. And I tend to agree.
But that says nothing about the economics of the situation, or the "fairness" of paying the coaching staff a market wage, or even the fact that these absurd salaries are, in fact, driven by a very liquid and efficient market.
http://budget.universityofcalifornia.edu/files/2011/11/2012-...