Just saying spotify for this example, but it could be any music streaming platform.

Twitch team would have to work with spotify to accomplish this.

-Streamer can control what everyone hears. (Except volume, and maybe some restrictions on how much they can skip so it's not jarring on the viewers)
-Viewers can thumbs up or down songs, if too many thumbs downs occur in a small amount of time, in contrast to thumbs ups, the song is skipped, or a skip request is sent to streamer. Feature can be disabled to prevent abuse.
-Song request queue. Viewers can request songs, and vote on other songs.

How it works is you join a stream, then the streamer has either a code to type into spotify, or qr code, or even a permanant room on spotify that people can just search for the name, maybe even a button that just opens spotify for you right to the listening party.

Pros:
-Avoid DMCA
-Integrated song request system
-Spotify pays twitch $$$ for this partnership

Cons
-Probably a lot of dev work from the spotify end
-Viewers that join listening parties that don't have premium would be interrupted by ads
-Viewers that don't want to join listening parties won't hear any music