At research universities most of the budget comes from research, and most of the work in research gets done by grad students. Undergrad programs are an afterthought.
That's only true for STEM fields, though. Outside of STEM, department's budget is actually correlated with teaching undergrads, so they tend to do a better job of it. Which is why so many undergrads end up switching majors away from STEM in college.
> And from what I can see most of the budget comes from and is devoted to college football.
This couldn't be further from the truth. I'm unaware of any major universities in which sports money comes from or is applied to general budgets. Athletic departments are generally self-contained and there is very little (if any) financial overlap into the academic portions of a university. Payroll, and even scholarships, are paid from athletic income, and any left over is not put into general budget.
Personally, I wish the myth of "the cost to the university/tax payers/etc" would go away.