We should have more than one type of civil war even.
The rebellions we have now where a city gets independent (and should have a chance to stay independent)
Separatist civil wars where a faction of lords disgruntled with their liege rise up to try and become independent (like the Rhodoks did when they split from Swadia)
Claimant civil wars where a clan disagrees with succession for example and try to gather support among the clans to crown a king of their own eventually splitting the realm into large warring factions (just like the imperial civil war but dynamically this time)
+1 - at the very least we should have Separatism and Succession Civil Wars which can be triggered if X% of lords have a negative relationship with the Ruling clan (maybe 25-30%, would need testing if this was ever taken up). Succession Civil Wars should trigger on split votes (or anything less than 75%) which would make them less likely to happen. It would technically be a sub-type of Separatism where you would have Loyalists and [Insert counter-party title here].
The Rebellion mechanic has infinite potential, I had asked @Duh_TaleWorlds about Minor Factions possibly raising to start their own Kingdoms and he said a feature like that wasn't planned right now - but I hope some more Rebellion expansion a la Civil War would be taken up.
Another idea is that the various Empire factions don't start split up and there could be a (better) main questline that triggers a static event where they split or stay united instead of the current main questline where you can "unite" them but that means killing everyone...