I've seen another 3D world already doing this albeit 3-8 FPS as it looks like it was injected into the actual game which this, like the mp3 DJ streams now, are not. Well, not really... And yes, I do see your point on some copyright issues but not from Big Mouse - Every streaming site has licensing for video streaming, just not VODs. DCMA is label based and in reality is not a legal platform against the user, it's an agreement with the streaming service to delete the account of major offenders, something a VR Chat program should never have to really deal with as it's never going to VOD or get the same insane high count of 10K users like YouTube, etc... 3DX could get a cheap-ass license for streaming via funds we pay and be done with it.
As for capturing video, another option if you don't capture Twitch would be do use something like MUX in the same way DJs use mp3 streaming sites. Again, the VJ absorbs the costs but a URL is provided which is could be passed to the 3DX client as outlined before. You just need to use OBS to stream to the service via RTMP. Simple to do... mostly
It can get costly - doing a weekly 1 hour VJ show to 250 viewers could cost around $110 and there are other options for people with $$$...
https://mux.com/pricing
I realize this isn't for everyone though - but would be cool.