So, have you considered putting the university events behind a game rule (the kind of all / only player / only AI / none rule), so that if someone wants to play with full historical immersion can disable it?
No, we haven't. As with all activities, engagement is optional: if you want "full historical immersion", you don't start the activity!
And there are so many opportunities for player involvement in this. Letters from your relative reporting that they're studying hard... or that they need money to cover their gambling debts... Letters from their rector suggesting that they should stay on for a doctoral degree, or in danger of failing (but that endowing a scholarship might make their teachers more sympathetic), or inviting you to endow a
professorship for a suitably eye-watering sum... Returning home with a friend they've made (perhaps someone who shares their scholarly interest, or perhaps someone who shares their bed). The player visiting their protege to see how they're doing (now that's actually a more realistic justification for a Visiting University activity...).
I agree with your basic point. But if the game is ever expanded to the Sinosphere (which I am opposed to but we know is planned), then it might want to engage with the Confucian tradition of the ruler-teacher, or in the usual jargon 'scholar-official': not teaching classes in a university, but engaging in scholarly activity such as writing erudite books as part of the ruler's work.
I think Areysak is saying that player relatives have the same chance as any other NPC to become a university teacher (low). That's disappointing, as it's something that medieval rulers would have been able to influence pretty easily. It should be well within the scope of
Wards & Wardens to add a version of
Ask to take vows that sends someone to a university province/large religious centre province, even if the devs can't guarantee that they stay there.
I love to see so much involvement with the feature and so many cool ideas!

Unfortunately, as with all activities, the focus is on landed characters, both for technical and flavor-related limitations, so only a landed character can initiate the activity of visiting a University.
That said, I do agree that there is plenty of space to expand the idea of University in other directions too, and I really like the idea of sending relatives and getting "reports" back! It is definitely out of scope for Wards and Wardens now, but it would certainly be cool to expand on the already existing decision to Send Child to University at some point.
You are correct, that is what I meant.
Considering that a University teacher needs to have very high education and skills, and that - as someone else has mentioned - usually you send relatives to take the vows because they are pretty useless and just an inheritance hazard, perhaps you wouldn't want to send these good characters away that often... And currently the way that wanderers work is a bit random, so we can't make them stay or go anywhere in particular, so it would be just a pretext to toss out good characters. So, to cut the story short, it is a good idea, but not something we can implement
as we would want to right now.
-What happens if you have a Tier 5 education and you go for another visit to the university and get max studiousness?
-I know others have asked this a lot, but will there be interactions to send family members to improve their education (or alternatively, bringing them with you when you do)?
If you have no room for improvement, you can't go to University anymore.
As said above, it is a very cool idea, but something that was beyond the focus and scope of Wards and Wardens. I can't promise anything, and it doesn't depend on me, but it is something that I would like to see too!
If i understand well, if we take our teacher back to our kingdom, he will give our character a XP bonus in its mastering attribute?
No, if you take the character back with you, you just gain an unlanded unassuming character with great stats that is either your friend or really likes you and that is ready to take up any court position or councillor position at your court!