Jabber is now XMPP which is a hugely used platform all over the internet for many many purposes including web and in-app messaging. It is fully interoperable between domains (if the server allows it).
It's actually also used by WhatsApp, only not in a way that suggests they will ever open up their service for federation (and why would they?).
So yeah, XMPP is part of the solution, but not if it's used in a closed off proprietary way.