No offense, but I think that is beside the point.
First of all, even in vanilla Warband, there where usually one or two factions dominating. But this happened not quite as quick as it happens in Bannerlord and the dominating factions where not the same in every playthrough.
Just as Tawny mentioned earlier, variety is the important part (although btw. I can't remember anyone proposing adding mounted tier II units to every faction).
In my current run it's (excluding me):
Khuzait>Battania>Aserai>Vlandia>Western Empire>Sturgia>Southern Empire>Northern Empire
(Though I intervened at this point already)
When I noticed the Khuzait getting dominant, I acted as a merc for any faction fighting them. If they'd make peace, I would search for another faction and so on. Even so I barely got them contained. But I'm fine with that, this time. I just don't want every playthrough turn out this way.
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In my opinion there is no way around nerfing them. Either their trait or their cheat or both are a problem. Also Blood griphons table is interesting. It might be a start to even out the max parties.
Also, if the devs don't want to remove the horse cheat, maybe it could be nerfed. There could be a secret horse stack in every village/town, only AI Khuzait lords can access by purchasing or looting. That way, they would still be able to get horses faster than other kingdoms, but at least they would have to do so.
Their trait could maybe only work in specific parts of the world. Then it would also make sense, that a khuzait lord basically would be faster (in the terrain he knows) with any kind of cavalry.