This is true - but professors provide the real value that students retain over time - so admissions fees should pretty much all be funneled to them. This is a problem with how hard to market the value professors provide is - a lot of admissions care more about a good sports team than a good set of professors even though the later factor will be much more important to them two years in.
Basically, people don't act rationally so the market is irrational.
> professors provide the real value that students retain over time - so admissions fees should pretty much all be funneled to them
I wouldn't so quickly ignore the additional tuition revenue athletics departments bring in at non-Tier 1 schools.
University athletics are a weird thing. But if the pay bothers you, think of it as a commission. Going cheap on that will likely cost more than it saves.
Basically, people don't act rationally so the market is irrational.