Actually this gets me thinking: what about making a signaling server for webrtc chats using IMAP ? This way we got a truely decentralised chat system.
This is how Matrix works, but using SRV records:
https://github.com/matrix-org/synapse#setting-up-federation
I've tried Matrix, and I feel it has potential, but right now the standard homeserver is slow and a bit of a memory hog. There are some on-going projects to develop other implementations, but they are far from complete, and not usable. I'm also a bit miffed why they didn't just choose the standard "user@domain" format for user identifiers.
Unfortunately message delivery latency has gone up a lot these days. It might be saner to ask, "can we deliver mail over MQTT?" instead.