(In this post I'm assuming mim was referring to using the character search function either to find attractive characters in other courts/realms for the purpose of inviting them to one's own court, or to just have them educate the kids in one's court.)
There's a lot going on here. The situation may have changed with conclave introducing favors; although I remember well people talking about how it was (too) easy to use this or that method to rope a foreigner into joining one's court many months ago, I could never seem to make it work quite that easily, and now favors have made the process of outright poaching somebody (as opposed to just having them teach one of your charges, as I'd generally done before, which takes time and may risk contaminating them with
foreign ways) basically foolproof. (So I'm assuming, having failed to get around to trying out conclave for myself yet.)
(
Edit: I thought I'd read somewhere that one of the favors let you force somebody to come to your court, is that actually so?) (Should've looked before I leaped, probably

)
Consider what taking away the option to obtain foreign education altogether would leave us with, though. A player (or any ruler, really) with a small realm may well start with a relatively bad court, and if they can't search for foreign expertise or at least some tutors, they might well be stuck with some sub-10 2-star councillors. That would kinda suck. I might argue unnecessarily so.
And also consider the intertwinings of the stat and education systems/mechanics: what can they be said to represent? In CK2, where human capital directly translates to the efficacy of the playable state (such as we play a state, vs a character, you know what I mean etc.), education, as in directly having one character teach another, is one of the only (relatively) reliable methods that the player can use to influence how good their character/state is at doing stuff (with marriage and personal decisions being a bit behind).
I can't speak to whether it would be accurate to have courts be basically stagnant unless and until they conquer territory that generates better courtiers (not sure how that works in general) or marry in somebody more skilled to do the job/teach the next candidates, but as somebody who enjoys the court management aspect of the game maybe a bit too much, as well as just the whole idea of playing as this reformer who takes their court/institutions to the next level and leaves contemporaries in the dust by any means, I do find the prospect of having those capabilities defanged to be less than ideal, both in simple gameplay terms and in concept.
Also, consider how much it would
suck in practice if any AI could favor your high-skill courtiers away without your say, like you can to them. (
Edit: again, assuming you can.)
(...I don't actually know, does the AI have favors to play with? Can they in fact already do that? Phew, really should've looked up at least that one beforehand)
...Although... I suppose with way of life, even if one had a full cabinet of jobbers, one could go through all of the stats one ruler at a time (give or take), taking a corresponding focus and leveling the ruler up to 4 stars (while presumably trying to also pick up traits that make for a good councillor), then educate prospective councillors until one has a good candidate to serve and to teach the next generation and so on, then move onto the next stat, etc.
That sounds friggin rad, actually. No idea how close it would actually be to historic, but it'd be a hell of a narrative, sure. Albeit a lot of work, especially for challenging starts whose survival is so uncertain that they need all the advantages they can get.
Then again, though, part of your original concern was that the AI didn't seem to be availing itself of the same options available to the player. If the AI has trouble with finding/poaching councillors as potent as the player can (and also, presumably, with educating its future councillors to an equal standard), would it be reasonable to expect them to go through all of ^
that? The gap between most AI courts and that of a savvy player might grow even wider.
I guess that's another root question: is the AI really that bad at assembling/growing a court? Personally I think a player ought to be able to outdo the AI enough to at least have something of an edge on them just on principle, but in practice is the AI so bad at it that it's not even a contest? I haven't actually looked at enough AI courts to know very well, but I can't say I've noticed the AI having, like, invariably dismal councils even in larger realms well into the game or anything.
(Sorry about the rambling post)