The "new" email has been launched quite a few times now. It doesn't seem possible at this point unless all the major players agree on some new protocol which is seamlessly implemented in their mail services, while still allowing SMTP to function as a fallback to the improved protocol
I'm not aware of any alternative email protocol that's implemented, except TMTP. I don't believe closed-source, walled-garden services, which don't allow third-party clients or servers, really count as legitimate alternatives.
There's Matrix, but that's a synchronization protocol for chatrooms, not a store-and-forward messaging scheme.
https://en.wikipedia.org/wiki/Dark_Mail_Alliance
The stuff Ladar Levinson created after the Lavabit takedown, (famed for begin Snowden's email provider). Although I'm not just talking about email protocols; but additions or other improvements that always have the same problems (PGP encrypted email, or whatever Facebook tried to do when they reinvented email...)