I think that, in addition to the AI being generally unable to handle factions, another facet of the problem is that factions themselves are sort of aimless and arbitrary. The way the system is set up, even mildly happy vassals will join factions, just for the hell of it. They don't really have a clear objective - they just want to join something. And so faction pressure is constant, rather than being a long term ebb and flow.
It's a tough balancing act - if factions only become a problem when a ruler is weak or incompetent or cruel, a human player might find that their genetically-engineered supermen never face a single revolt. On the other hand, if factions are a constant fact of life, enough to keep a player on their toes, the AI will fold to the pressure almost immediately. If the faction force is strong enough to break up an AI empire 100 years from now, it's also strong enough to break that empire up today - because faction strength will generally be constant.
I'm not sure exactly what the answer is, but it definitely is not in a good place right now. Maybe if there were more faction goals that were a little less destructive - some other options of similar consequence to liberty factions - and the AI could just concede their demands as necessary, it would be a little less chaotic. Maybe as we get more systems to interact with, like the upcoming court features, there will be more opportunities for mild factions. Right now, since most faction types (peasant, populist, independence and, to some extent, claimant) lead to border gore, any increase in faction strength will necessarily induce even more of what we see in these screenshots.
I envision a system where, over the years, factions slowly eat away at the king's authority, bit by bit, weakening his grip on the realm. Once the monarch is particularly weak, the AI will seek independence. This way, disintegration would still happen, and factions would still be a constant struggle, but it wouldn't be a sudden jump from "the king has one less levy than our hodge-podge faction" => "the kingdom is now 10 independent counties, and a swiss-cheese rump state". We'd see something more like what happened with the Abbasids in real life. As the caliphs lost power to their vassals, viziers, and generals, they grew weaker and weaker until whole chunks of the empire (Tulunids, Saffarids, etc.) were able to break off. It's probably the sort of thing that would need it's own entire DLC/patch to focus on.