When money is donated to the university, it is categorized into buckets like facilities, capital projects, scholarships, salaries, etc. Some of these things get spent right away or put into a fund that is spent over a short period of time. But certain categories, like scholarships, faculty positions, and some staff positions, can be endowed so that they live on in perpetuity. These endowments need to be large because they fund these based on the capital gains of the investment. The university I work at has almost 200 endowed faculty positions and a TON of endowed scholarships. You need a large investment to have enough returns for to function given market fluctuations. Our board of directors is tight with the endowment because it is a well oiled machine does directly impact the students - and yes it does affect tuition in the form of financial aid grants. It's long term investment and anybody who invests knows that you don't fiddle with your investments for short term gains.
The main cost of tuition is keeping the university running. Most faculty and staff positions are not covered by endowments. Our endowed faculty is under 10% of our total faculty and staff count. Students want less students per class. They want better access to professors and not to be taught by assistants. They want every electronic service imaginable. Both students and parents want electronic front ends to everything. The IT staff to support all of these is not cheap. Universities are not the universities from 50 years ago.
Those edge case high salaries are a pain, yes. It irks me when I see our president's salary publicised. But, it irks me from more of an honor sake. When our university says it is trying to adjust our operating expenses to give the lowest tuition possible and those insane salaries remain untouched, it is somewhat hypocritical in my eyes. In reality though, I don't see it making much change in tuition for the students. Say there are 10 employees making $1M a year. If we cut that in half, that is $5M a year that can go towards a tuition cut. That's huge if you have a school of 500 but nothing if you have a school of 20k. But, from a PR point of view, it affects perception. Coaches have a different job and can get whatever salary they earn because they are a money generating entity all in themselves.