So the question is really not whether there is an opening for a Twitter alternative and what features we would want it to have, but rather why the existing alternatives with strictly more features failed to catch on.
My take is that Twitter had already passed a threshold by the time these alternatives hit the scene, and their first-mover advantage carried them a long way in defending themselves against other similar-but-incompatible platforms.
Put another way, the reason Twitter is singular and email providers are not is that email providers communicate with each other over a common open protocol, whereas Twitter communicates only using its (closed) API.
The difficulty would not be in defining an open protocol to doing what Twitter does, naturally; existing ones could be tweaked slightly to achieve the same result. (Look at what Shortmail is doing while maintaining 100% backwards-compatibility with traditional email).
The problem is that Twitter has no incentive to turn its "open" (read: closed) API into an completely open means of communication like email, because doing so would squander the one huge asset it already has: a captive userbase.
(For the record, the same arguments could apply just as well to Facebook; people just don't think about Facebook that way, because we're all so used to them being a walled garden).