That sounds somewhat like the university of austin, or whatever it's called. They're launching this fall and trying to get accredited. It will be interesting to see how that plays out.

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.

I agree with the general thrust of your argument but it's oversimplifying the causes. A real university would not be able to run with just professors and secretaries, that's ludicrous. You need some administration to handle compliance, organization, finance, etc. You can both acknowledge the objective reality that a university is a complex organization that needs administration and that most universities today have 3-4x more administrators than they need.

And why couldn’t the professor or two who teach finance be responsible for the university’s finances?

Surely you're not implying that every person with a PhD in something is an excellent practitioner of that thing. Most aren't. They shouldn't be - their job is primarily research on that thing, and teaching that thing.

Not every finance professor can manage a multi-billion dollar budget, not every Political Science professor can manage a campaign or run for office, not every Comp Sci professor can maintain a university network, etc. Not to mention the fact that not every college will even have a professor for every discipline that you could theoretically use to replace an administrator.

> and research

Why research? Why not go further and cut that bit out and just leave teaching?

I'm not convinced that the best place to teach student is necessarily the best place to do research at, and I'm pretty sure that your competence at being a good researcher has very little to do with your competence at being a good teacher.

Because the purpose of a university isn’t teaching. And you really cap yourself at undergraduate education if all you want to do is teach. Not is the purpose of professors to be good teachers.

There are hundreds of colleges. That's competition. Why aren't any of them competing? Because there isn't actual profit in it. Except for the for-profit colleges that do exist, do compete, and occasionally get shut down because they turn out to be scams.