I think the core problem is that Twitter should be a protocol, not a company. There's just no need for there to be any servers: users could send messages to one another, each running his own agents.
Since the Twitter experience doesn't need the Twitter corporation, there's always going to be friction and centrifugal force.
Even as a protocol, there'd still need to be some means of governing the distribution, storage, and retrieval of tweets. A simple P2P network would make it much harder to gain a foothold when nobody is mirroring your content.
I think Twitter the corporation could make a viable business of filling that role by selling access to infrastructure for the protocol to developers of end-user applications and various data hounds.
Since the Twitter experience doesn't need the Twitter corporation, there's always going to be friction and centrifugal force.