Professors don't make much these days, but check out the salary for university administrators in the US. The top of the food chain has quite nice compensation, and the amount of administrators is probably too high.
Universities also compete on who has the best food and nicest dorms. Prospective student often tour campuses, so having a pretty one with lots of rose bushes, ivy, and brick is good for recruiting. That all costs money.
Another thing is that elite private universities often have strong need-based financial assistance (discounts). MIT, for example, claims that the average need-based scholarship is about $47k (on tuition of 53k). They also claim 31% attend tuition-free.
Making a small inference: Those who actually pay the full $53k in tuition are helping those who pay nothing.