Multiple Audio Tracks
This is a rather complex idea which would need the cooperation with the streaming program developers.
Idea is to have a system where you can stream two audio tracks instead of only one, giving the possibility to the viewers to separately change the volume of game sound and streamer's voice.
This would of coures increase the load, but since the video should be the biggest part of streaming in most cases it shouldn't be that big of an increase.
I stream with my brother, he lives 1500kms from me so we use Discord to chat, unfortunately he has a bit of a hard time with it because of the echo from hearing his own voice.
Ideally I'd like to run a second, possibly even third audio stream for him so he can turn his own voice off, and potentially my voice off (since he can hear me on discord) without the echo.
I think this would make the most sense for a music track that can be muted or reduced in volume for viewers who do not care about the music, find it distracting or would rather listen to their own.
Also, OBS Studio already has support for multiple audio tracks.
It's a nice idea. Like you say though, you'd need the cooperation of the people that make the streaming software.
I could see it theoretically happening in OBS-FTL, but as for standard OBS, Xsplit, etc...I doubt that's on the cards.