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)