I think it largely depends on what you’re playing and what you’re doing. Super casual stream, and you’re playing a game where there is no voice chat between teammates/opponents, and it’s an RTS/Moba where audio queues aren’t generally terribly important, then sure, toss on some music, but only as background noise.
If it’s a game where audio queues are important (CSGO, PUBG, Overwatch, etc.) and/or you’re playing in a competitive environment, I say game audio takes priority. Especially when there’s other voice communication that may be important to hear. For the most part I’d say game audio on it’s own is perfectly fine.
I don’t watch many streams but in the past I’ve watched CSGO, and Destiny streams and I enjoy hearing the game audio rather then music. It allows me to get more involved in the game, and when watching higher level play, it also can help me learn what audio queues the ‘pros’ are using. If they hear certain things to their right and react accordingly, etc. Having music overlay that makes it difficult and you start questioning why they reacted in certain scenarios. Again, for that it’s more of a competitive zone and the audio queues on those games are important.