I just thought of a number of faction ideas. These would be cults for the Daedric Princes. Now, you would be able only to join one cult and would fight with cultists of enemy Princes. Joining a cult would be an easier way to obtain the artifact of the prince, but you would still be able to get the others, but doing a much harder quest. You would also gain the ability to ask fellow cultists to help you (i.e be your follower) and would have radiant assignment for small quests. Each cult would have its own story line and you would try to kill as many enemy cultists as possible. This wouldn't mean members of other cults, but only members of a Daedric Prince's cult that yours specifically dislikes.
This is for TES6, not Skyrim. It would be a waste to do it for Skyrim at this point.

...Why do all these faction idea's have to do with having some sort of beef/war with another?

It's not the whole story, just that your Daedric Prince hates another Daedric Prince and wants you to kill their followers. The story would be more about getting their artifact or learning about it and things like that.
Don't tell me you don't want to do some sh*t for Sheogorath!

Already did. And I highly doubt they'll rewrite the game as to alter the Daedric quests now.
Maybe better luck 5 years from now when TES6 comes out.

Not now, I was meaning for them to be in TES6. Guess I should have said that. I'll add it to the OP.

Worship me and I shall set ye free.

Of course you did.
Either way, being a Daedric Prince's toady can only entertain me so far. And factionism annoys me as a gaming convention. Naturally you join a faction, and totally have to go fight another faction because reasons.
Children and their war games.

I swear. Daedra's honor...nevermind, Daedra don't have any >.>
I mean, you don't HAVE to fight them, it'd be more of an OPTION to do so.