Oh come on beni, you of all people should know better than that.
The emperor is a puppethead. The Dark Council controls the empire, THEY are the leaders. The emperor is something to rally behind, but he controls nothing. He sits off in the unknown plotting to destroy the galaxy. That is all he does anymore.
But symbols are powerful things. They can grant hope in the darkest hour, or crush that hope from ever forming, and they can bind things together either from great respect or great fear.
I would also argue that whatever the emperor wants, he gets. Just because a manager runs a store for the owner, doesn't mean the owner can't get rid of him and put someone else in that runs it more to the owners liking. Same holds true for the Emperor, he doesn't micromanage his empire, he gets a bunch of guys to run it for him, but if those guys get delusions of emperorhood or start doing things he really doesn't like, then they wind up greasy stains on the floor and he gets a new guy to fill the spot.
Honestly, i think they would manage.
Even with the emperor there is mass infighting in the dark council...
Without the emperor, i'd see Mortis, basically in charge of law, or Marr take the lead. That or Darth Knox and the Wrath together.
If thats not possible, Knox. Pyramid of ancient knowledge seems like something an emperor would be the head of, and shes probably the most powerful other than the Wrath...
The mass infighting serves a very good pupose, as long one's minions are busy fighting among themselves then they're too busy to join up to challenge you. Also, the fighting keeps your minions sharp, the weak or stupid die and are replaced by new minions, who either keep up or join their predecessor in the corpse pile. All of which works to the advantage of a Sith Emperor.
Of course with the Emperor dead it creates a power vaccum, and sith being sith will try to fill that power vaccum. Remember, loyalty isn't strong with Sith and none of the Dark Council would willing bow to another one. Only reason they bowed to Vitiate was because he could reduce them to a greasy spot with a thought, that and the fact that he had an army of super strong brainwashed minions ready to die for him.
So a power struggle would likely have several members killed, with the rest splitting of and using their individual powerbases against one another leaving them vulnerable to who? The Republic. If left to their own devices a leader might emerge to unite them again, but there's no way the Republic will give them that time. (though, of course, limited factions would survive, though too individually small to challenge the Republic head on)