The hardest part is not the client and the server...but the CRM (the Intercom part). Here's something a lot of us would use - we want to bring our own socket API (for example pure websocket, xmpp or something like Pusher.com ) and connect it to a full fledged Intercom-like tool.

This is the "Gitlab for Intercom". The problem that happens is that people usually don't want to rip out their client side messaging SDK, especially if you have a mobile app.

I am personally looking to pay for something like this (we use Pusher.com internally).

Are you focusing on the socket server or the CRM application (like Intercom) ? Because the socket server part is a don't care for everyone. Pusher or Firebase is super cheap. It's the CRM that's tricky. Smooch is one end of the spectrum and it focuses on integration with other tools (helpscout,etc) while Intercom is obviously a CRM. I don't think you'll be able to build both.

If you can build this out with excellent featureset like Intercom and can integrate with something like Pusher (and not lock to your own server), I'm gonna throw money at you!