This simply isn't true. Most people don't know how to use email, which is why these stupid memes of "everyone hates email" and "email must be destroyed" persist. What people hate is email being used in a dumb way. Or to be more blunt: People hate dumb people. No surprise there, really. So a solution is to get better at getting rid of dumb people. One way to do this is to persist in using email well, and demonstrating (with persistence and persuasion) the better way when rolling across crap use.
This is one of those (rare) situations where the technology and infrastructure is fine; the people using it are the problem. Email can be incredibly effective when used correctly.
Mind you there are certainly email clients which make it far too easy to use email poorly.
Which is not to say that you don't have a point either, but rather just that your assertion of "simply isn't true" well...isn't true.
The conclusion is still the same. This won't solve the "problem" with email.