Depends on what you call major. But it certainly isn't just Oxford, Harvard, and the like. Pretty much all US "University of X" (where X is a state) have their own presses.

Yeah, and see, I'm not claiming that the University of, say, Wyoming, has the money to keep their own press running. But the Ivy League, Stanford, MIT, and the like... they definitely do.

They usually cap the number of books they publish a year. Artificial scarcity makes their imprimatur more desirable.

Lol, we have the opposite problem—we need to have more books.

If we want to have more books, we need to protect the rights of the publishers—if publishers are not protected, then the market is just doing its job: publishing books is not going to be profitable if book contents are stolen without consequences. As a result, universities wouldn’t want to waste money publishing books, and for-profit journals would have to charge exorbitant subscription fees to compensate for the fact that no one except a few institutions will sub in the first place (everyone else will get the same stuff washed through an LLM).

The barrier to publishing a book is more or less non-existent. The barrier to getting a publisher’s name that is sufficient for someone to think (rightly or wrongly) that this book has a legit stamp of approval is somewhat higher if not all that high. And obviously implies that those publishers have to gatekeep to some degree.

Sure, we turn away crap, but so what? We don’t have a cap on how many books we can publish other than the time, labor, and money resources we have. Which are finite. We could publish more than we do now, and we have in the past.

For sure, but do we want the academic publishing landscape to be an oligopoly?

This is the current membership roster of the AUP:

https://aupresses.org/membership/membership-list/