It prompted a lot of Q's in the comments, so I've assembled an FAQ to address them:
https://mnmnotmail.org/faq.html
More questions welcome!
[1] https://news.ycombinator.com/item?id=25804869 (not in Show HN)
You describe the problems correctly, but your solutions are very shallow.
"Don't store delivered emails"? Great, now we need to do backups of all the individual mail clients!
"Instances that can't be accessed from outside". What happens when such an instance gets compromised? And now _everybody_ on your internal network, who trusts this system without a slightest doubt, will get massively owned.
And on and on it goes...
The TMTP server supports replication to multiple clients per account, which enables backup. I note in the FAQ that servers may perform archiving (which is not the same as retaining all the traffic).
Any network information system could be compromised. Zillions of them are trusted. If you're alluding to E2EE, see the FAQ.
Mnm has no global identity and no federation - so what this protocol really replaces is either non-federated chats like IRC or Slack; or internal message systems like the ones found on bigger forums.
FAQ: https://mnmnotmail.org/faq.html
Twitter: https://twitter.com/mnmnotmail