I studied at a "startup university" that had just a few dozen professors. The total number of employees was still more than 100, and it wasn't all "bullshit administration".
There were assistants to the professors (1 assistant per 3 professors), the bigger research groups had post docs and lab technicians, there was an IT team (3 people), there was one person responsible for the sign up formalities of the students, a director of the institute, his assistant, one HR person, 3 or 4 people in the cafeteria, cleaning staff, head of microscopy lab, some scientific support technicians, people feeding rats and mice in the life science facility, a few people in the machine shop, a librarian (library was digital only; still took a dedicated person who made sure everyone got access to the literature they need), and those are just the people I met and remember.
That university only offered PhD programs, so there were only few lectures. If you wanted to do undergraduate courses as well, you'd need a lot more people than that.
Universities just need a lot of staff.