Weighting does work, it just needs to be done right.
Take a look at this (
https://forum.paradoxplaza.com/forum/threads/mod-imperator-invictus.1473328/page-82#post-30180040) and tell me that you don‘t come away with the conclusion that weighting can fundamentally and conceptually work, but that PDX just screws up the implementation (for whatever reason).
I agree with:
The other reason why it doesnt quite work in ck3 is coz there're a lot of options that are just plain worse than other ones and the general balance is quite bad. Like, cattle pastures are just better hunting grounds, sure, the latter one is a bit cheaper and gives random non-mattering bonuses, but in terms of main stats that are tax, levies, garrison, fort level and development hunting grounds are just worse. All that meanwhile wheat farms in the current balance, are just better cattle pastures. Coz they cost the same and give more tax, sure they dont give levies, but do you care for levies?... No.
And same kinda applies to military. Countering doesnt really work, terrain penalties dont scale, economy has no sinks so cost doesnt matter much either, so better stats = better MAA, plain and simple, AI however is made with those things mattering in mind, so it weights in synergies like adding archers to heavy infantry comp to counter skirmishers that counter heavy infantry, or picking more cost effective MAAs for smaller realms. All of this just makes AI worse, not because weighting doesnt work, but because the balance that the weighting assumes is just not there!
As I said, not everything is black & white, but some things are, any weighting to parts of the system in which there is one right answer, and every other answer is just wrong to different degrees is bound to fail, in different degrees.
Forgetting CK3 for a moment as Benismann's example was good enough let's use Stellaris as an example.
Weighting can create dynamic interactions between empires, making them behave less predictably, in one game the militaristic guy can act as your protector and great ally the entire game, the next match the same nation may feel you're a valid target for expansion and become your worst enemy, that's where weighting shines.
Where it doesn't is in everything related to build orders, development templates or most military afairs, having a chance, no matter how small, of having an artillery ship adding short range machinegun turrets is always going to be detrimental to ship desing, likewise having "varied" fleets which I often call shit-sallad templates replaces actual variety such as a torpedo fleet fielding nothing but frigates, another, harder hitting torpoedo fleet using nothing but cruisers, perhaps a missile cruiser fleet using long range computers to kite oponents, or a disruptor fleet using only small mounts and fast engines, or even the traditional artillery battleship fleet, all of those possible designs are replaced with the near identical "shit-sallad" template, in which every single fleed must have equal numbers of corvetes, destroyers, cruisers & battleship, and every ship must include a bunch of mismatched weapons that are equally inefective at every range.
The end result is, of course, an AI that can never be challenging as any actual fleet, with a purpose to it's design (doesn't have to be meta, any design will do, as long as there is any planing involved) will beat them.
On the other hand it substracts from the depth of the game, as you will never have to think about what the AI is spamming so you can try and counter them, so you'll never really "have" to retrofit your fleet to change the way it fights against a new enemy, the only enemies in the game that make ship design relevant & interesting are the endgame crisis, and the reason why they do it is simply because they have no weights whatsoever, they all follow their own hyper focused ship templates, so you know what kind of weapons and defenses you should bring against them. Before they spawn the ship designer is largely pointless feature, as it isn't necessary, that also spoils the fun of the game as you know the AI will never make use of it to counter anything you may want to try. A wasted feature.
I don't think any sort of weighting could fix such issues, having any weight, at all, to sub optimal/bad choices is only going to decrease the quality of the experience.
Of course you can have a weight system for the AI to chose which templates it's going to use, so France, as an example, may want to use a heavy cavalry build most of the time, but sometimes they may surprise you showing up with a proper, functional heavy infantry build instead, that would be interesting.
What's not interesting is a bunch of mismatched MAA that don't really focus on anything, can't be the focus of anything, and don't particularly work, as we're seeing everywhere in the world.
Of course, this also applies to development/economy as the post I quoted above says, everybody needs money and having more income earlier in the game guarantees a strong mid-late game, I can understand the choice between focusing on develpment with a learning focused build vs stewardship and building better buildings faster, but there are also terrible choices the AI can take.
IE: Building fortifications everywhere outside of their capital counties, not rebuilding bad templates to suit their needs, not having at least one good military building to boost the MAA they have built, or simply chosing the clearly inferior options for no real reason other than "it was rolled at random".
In a proper game the player should never think "Look, I'm clueless, I just started the game and the AI is building random junk just like me", he should be thinking "Ok, I just got beaten up because I had a bad opening, how do I optimize this so I can catch up to the neighboring AI?", figuring this out, then being able to apply it, and then trying to find other ways to get the upper hand to break the tie is what makes strategy games fun.
Edit: Oh, and there is one army that looks half-functional in CK3 too, for the same reasons seen in Stellaris, the Mongol Army, they spawn from a template, making a coherent number of MAA, the AI still fails to properly station them to grant them bonuses but just having that is enough for them to trample over all the other AIs in the map.