It does feel like there is an easy solution to this:

Have tests.

Supervise said tests to make sure people don't cheat.

That's how it worked when i was in university. Admittedly maybe that is easier in the sciences than humanities, but still, it seems doable. Cheating isn't a new phenomenon it just got cheaper and easier.

The tests will be made by AI as well, because professors who spend less time on making tests can spend more time on research and get hired/promoted more. For the same reason, professors won't care who is using AI to cheat on the test that was made by AI. Maybe some people will care, but not enough to do anything about it.

(Cheating was already rampant in many classes 20 years ago when I was in college, I can't imagine what it's like now.)

This selects for people who excel at taking tests. Sure, there may not be a better alternative, but as an empirical measure I learned just about nothing in my test heavy college courses, as I was incentivized to cram for the exams and purged everything immediately after the final (and midterm).

OK but why? That will reward students who are good at taking exams, which has very little relevance to being a competent worker or well-rounded citizen or innovative leader or anything else that we need.

Right? It's exactly how we train AIs, after all. It's not like this is mysterious.