Even iMessage seems very much like a 1-1 messaging system.
So no, at least SMS is not a social network.
I don't like WhatsApp anymore but it was in its time my favourite social network. I had all my important groups there, used it exclusively to communicate with close friends and family.
It was the place were most images were shared and discussions were held and so on.
“Depending on your settings, you can also periodically back up your WhatsApp chats to Google Drive”
“You can use the export chat feature to export a copy of the chat history from an individual or group chat.”
I haven’t checked the full backup, but exports of individual chats are easily readable (zip with a .txt of all texts in the chat and individual images, IIRC)
The individual exports work fine, but it’s very tedious to go through every conversation individually.
Slight aside: keeping a TCP connection consomes almost nothing. In fact, that's how push notifications work today on Android: a TCP connection is kept open, and apps' server send a ping to Google to tell the mobile to wake up.
What prevents power-saving is if every app keeps a different socket open to a different server and pings the servers on different schedules. That forces the mobile to wake up constantly.
It would be interesting to see whether Facebook/WhatsApp and iMessage have made them desperate enough to reverse course on XMPP but I'm skeptical that they'd be trusted enough to be successful.
¹ https://mail.jabber.org/pipermail/operators/2013-February/00... and then https://mail.jabber.org/pipermail/operators/2013-May/001680....