Most social services we use today could be streams. Facebook, Twitter, even WhatApp, Instagram (I guess not snapchat). If they'd all implement some common stream spec. Unfortunately they won't, Twitter has demonstrated that they don't like alternative client implementations.
If it could replace e-mail is another big question. Nikita hilights the amount of cruft that's around e-mails, but the cruft is social protocol, and we humans love social protocol. Or perhaps that's just old fashion speaking.
The posting is quite old already (Oct 2014), so this isn't some big hype building and it doesn't look like anyone is working on a big implementation.
Technically, the standard XMPP PubSub protocol with its PEP companion could get you very far already, unfortunately there's not many clients that handle them today.