It's been attempted, but the issue of storage remains the most bothering. A mailbox can be pretty big and having it distributed over the network is difficult. Not to mention spamming problems.
Maybe some day we'll find the right formula. But I think the who-owns-the-private-key problem is a bigger priority.
Not for nothing, but Usenet is a distributed email system. Yes, most people use it as a forum or a file transfer system, but once upon a time it was a way to send email. One downside was that people had to locally find a path for routing their mail through the network, though I suspect that with modern techniques that would be irrelevant. Storage is not an issue if people can download their mail. Privacy is achieved with public key encryption, authentication with digital signing.
The real issue is not spam (which is already manageable with modern spam filters), but the fact that you need to download your mail and store it yourself. That does not really mesh with how people are using email these days. This is, in my view, the big stumbling block to strong encryption -- people are frustrated by systems that prevent them from reading their mail on their friends' computers (or kiosks, etc.).