Very interesting data ! I wonder how you achieved that. I guess some early modding !
My take on this and what I've seen in my own playthroughs is that there are two solutions to this particular problem, one that I prefer massively.
1 -> Balances and "brute force rules" applied to AI in order to straight up prevent this from happening IE making dominating AI dumber, giving a bonus to armies that belong to struggling factions... Basically what you'd call a band aid to the problem as opposed to a proper cure. I'd see that being done short term so as to not slow down testing on all the other aspects of the game.
2 -> Understanding the fundamental problem with the simulation. That's a lot more complicated, and if ever a proper conclusion is reached it's going to take a lot more data, and a lot more thinking and debating.
For that we can step away from Bannerlord "the game" and enter Bannerlord "the simulation". What happens if the player doesn't ever do anything ? You've collected some data on that : one or two factions swell in power and almost never get stopped. There seems to not be a single mechanic that can stop a strong faction's momentum other than the diplomatic AI deciding to have peace for a while. The speed at which this happens has to be noted too.
From what I've observed, here's what I think : it seems way too easy for factions to gather their strength together and put all their might towards one goal : total annihilation of the enemy, taking all they have. On top of that, the new territory can immediately feed the war machine : there is no mechanic such as "core territory" or "cultural integration" or any real debuffs to how much newly conquered territory gives to a faction compared to the heartland.
So the solution is twofold : splitting each faction's might into multiple, sometimes conflicting goals, and avoiding systematic recovery and strengthening of a faction's war machine without some time of stabilization.
The first solution is probably the most complex to actually get to work. Luckily, there already seems to be a pretty strong framework of vassal and clan individuality within kingdoms. Moreover, with the possibility of characters dying of old age, it stands to reason to think every single system related to characters is dynamic. Mechanics involving changing the ruler of a kingdoms for example shouldn't be game breaking.
With that in mind, I would propose that the Clan layer be used more. There is no reason why clans should never fight eachother, even within kingdoms. Clan conflicts with each clan belonging to different kingdoms could also happen without the kingdoms themselves acknowledging them of course. If rulers had to spend a lot more resources to fight internally as well as externally, it'd take a lot longer for any faction to become united enough in their goal to start steamrolling anybody. On top of that, it makes sense being steamrolled would be a strong unificating factor, wherein lies your "comeback" mechanic for struggling factions. Outright civil war could also trigger (tho should stay rare, lest the game become confusing) where a faction could splinter along its clans.
Finally, extinct faction that still have "loyalist" anything (freshly defected clans, freshly conquered towns...) could rise from such inner conflicts and come back into the game. Clans could also outright create their own kingdom... after all, doesn't Warband take place only a couple hundred years after Bannerlord ? If the ambition is to have generations-spanning playthroughs, where are the mechanics for the Khergit Khanate or Sarranid Sultanate to form ?
The second solution is simpler. From the lore it's reasonable to infer Calradia does not share a single culture beyond language and the love of butter. As such it'd make sense for towns to have cultural preferences as far as their direct and indirect leaders go. When placing a imperial cultured lord to rule over a Battanian town, himself being a vassal of a imperial ruler, the local populace shouldn't be as willing to enroll into armies or pay taxes. Some notables could outright decide to "resist" and create more banditry in the countryside aswell as redirecting caravans to trade away from these towns.
I think as I write... where are notables in all this ? What would prevent the system from letting notables (especially gang leaders) from staging rebellions and proclaiming themselves as independent clan leaders ?
Tons of ideas in my head... but ideas are a dime a dozen as they say.
TL;DR My main goal with writing this wall o text is to argue for not (in a durable manner) putting in brute-force mechanics to artificially curb strong factions with the pure goal of "player experience". Playing into the deep simulation and emergent gameplay might seem like uselessly complicated to solve these problems but they add much more to the game than band aid solutions.