To say that the overhead goes to flashy buildings and fat admin paychecks is a bit of a misrepresentation. Those buildings almost always have a major donor and a substantial endowment component. The academic (especially physical and biological science) divisions do actually need to pay for office space, lab space, heat, staff to run it, clean it, make the computers go, etc. If you think my salary was ballooning while building and running everyone’s HPC clusters, I can assure you it wasn’t in any sense other than perhaps slowly deflating over time. Compared to whatever the football coach and president are being paid, there are thousands of people on staff who aren’t getting those fat paychecks.
Try 90% and almost all of it goes to the football coach or the dean’s legal fees.
https://osp.mit.edu/facilities-and-administrative-fa-rates
HMS declared rate is 58% but there are a lot of loopholes (as at other R1s with Institutes)