This actually makes a lot more sense that it did a decade ago. Mail servers were needed in a time when we were not always online. Now that we are, we can technically run everything that's done by a server on our own PCs. The bandwidth and processing power now exists. The resulting setup would be a peer to peer network with nodes connected via address/name servers.

For those times we're offline, it may be possible to spin up a temporary cloud instance which downloads everything back to us and dies once we reconnect.

The only question that remains, then, is backup.