Spotify, YoutubeMusic and other platforms are able to provide licenced music via a 'fee for service' model, with pricing typically around the $12-16 price point.

Twitch's platform adds another layer of 'complexity' here, in that the music played would be heard by more than the single user to whom it is licenced under a standard subscription fee. In almost all case studies for music on streaming platforms, the main problem highlighted is the plays/count and artists not being compensated accordingly.

Suggestion 1:
Twitch provides a subscription based service enabling users to play mainstream music, without restrictions. This fee would perhaps/logically be slightly higher than a sub for other similar services in recognition of the 'replay' aspect of the track. For myself, I know I would be quite happy to pay $20-25/month, an increase of $10 approximately over a Spotify or Youtube subscription cost, for access to streaming said music without being muted.

Suggestion 2:
Twitch implements a subscription services, linked to Soundtrack?
I.E If I am streaming, and have a paid subscription - I can play mainstream tracks which are audible to other subscribed members. Individual users without a Soundtrack subscription would not be able to hear the audio?