I don't remember ever being asked for my vaccination records when I attended college. It's not like you need those vaccines which you mentioned every year. They're pretty much a one and done deal. You don't get dis-enrolled for not having the Flu shot and that's just as dangerous as Covid for kids of college age.
Point taken.
With the exception of the last one - Covid is more dangerous than influenza for anyone of any age. The data bears that out pretty clearly.
That said, I'm not 100% in favor of Covid vaccine mandates at this point, since the vax is available to everyone. Unvaccinated people introduce some additional risk, even to vaccinated people, but it's pretty small, I think.