The highest paid public employee in my state is a college basketball coach.
I think it's less about the amount any one person is paid and more about the huge number of administrators moving paper from one desk to another.
I went to a private liberal arts college with a few thousand students. We had a Dean and four assistant Deans, all of whom made multiple six figures a year. Our president when I was there made $450k/yr and had next to no living expenses.
B.
Private v. public has nothing to do with academic bloat.
But Big 10 football (and basketball) runs at a profit for the schools, it's the big salaries at smaller sports programs that don't make financial sense.