When people say "It's broken" what they often mean is "It works both ways".
That is to say, the power granted by email to ignore others, send badly composed missives, avoid direct engagement, and conduct extensive time-consuming posterior-covering is (horrors!) mirrored by other people's ability to do the exact same things in return.
Ultimately, any "solution" that "solves" these problems satisfactorily will do so only be frustrating others, while leaving the people with the "improved" version free to go on doing whatever irritating things they've always done in a world that can no longer push back.
EDIT: Ok, perhaps there's more to email being broken than the social problems that are beyond the scope of technical fixes. But honestly now, how much?