The optimal university contains only an admissions office.

And a big bank account for deposits. When you want to hire someone that can show off their $100k+ proof-of-burn, you probably need to pay them well. They’ve demonstrated that being paid in peanuts won’t cut it. They mean business.

Who manages departmental needs for majors that require equipment (STEM) and audits the expenses? Who hires and does a Background check of these auditors and admission officials and professors?

I have often felt this. The skills learned are of little direct value, but the qualification is signalling enough. I mean how much different for a middle management position is I got accepted to Harvard and I graduated from Harvard.

"The Case Against Education" by Bryan Caplan lays out exactly this argument:

"Caplan argues that the primary function of education is not to enhance students' skills but to certify their intelligence, conscientiousness, and conformity—attributes that are valued by employers. He ultimately estimates that approximately 80% of individuals' return to education is the result of signaling, with the remainder due to human capital accumulation."