For a private screen you can use a web based solution like mirotalk or jitsi. Pretty much all web browsers support screenshare via an extension these days so its mostly just a matter of finding a server with low latency (or running your own) 

I tend to stream directly to peertube so thats what i was thinking of for obs but its true that obs isnt ideal for smaller private sessions.

No, what I am saying because that functionality exists within OBS, it can be redirected/repurposed to directly stream the video through another application/protocol entirely (although if that's already release ready is up for debate).

The proof of capability is there from the pre-existing Youtube/Twitch use cases, but there's no reason that OBS couldn't work as well for something like Matrix (but the groundwork may not be ready yet).