Have you not heard of https://matrix.org?
100% open source server + client(s), decentralized, federated, easy to stand up your own server, end-to-end encryption, bridges to tons of other networks (IRC, telegram, slack, mattermost, etc), full history sync even when you log in from new devices, read receipts (even for individual users in group chats). They're by far (in my opinion) the most feature-rich of the "new-age" communication systems. I've been running my own homeserver for over a year now and I can't recommend it highly enough.
Federation of self-hosted servers and the "official cloud" seems to be on Wire's road-map, cf:
* Third paragraph of OP
* https://www.reddit.com/r/selfhosted/comments/5vylls/wire_end...
* Last sentence on https://medium.com/@wireapp/open-sourcing-wire-server-code-e...
Nope, just Electron.
Some people use it that way sure, but they're wrong. You can either help point it out when they make the claim or you can be a part of the problem.
`Whisper.Backup.backupToDirectory()`
`Whisper.Backup.importFromDirectory()`
What's the use case for self hosting ? Since it's supposed to be e2e, does self-hosting buy you anything ?
I also like the fact that Wire doesn't need a phone number (unlike Telegram, Signal, WhatsApp and similar applications). You can sign up with an email address and use it. Of course, Wire is end-to-end encrypted, syncs across devices (unlike Signal) and has native^ multi-platform/multi-OS support where each device is independent and doesn't need the phone to be around (unlike Signal or WhatsApp).
On the topic of open sourcing the server, it's a good move from the security audit point of view. But until any of these new age apps/platforms support federation and decentralized communication, there's not much use for the masses to look for servers run by specific people.
^: As mentioned in a comment below, it's an Electron app, but I meant to indicate that there's an app that you can install for each platform without having more prerequisites (unlike Signal that requires Chrome/Chromium to be installed first).
[1]: https://wire.com