Exists, Pretzel.rocks, monstercat, Jamendo amongst others.

Can't recommend pretzel rocks enough. They have a great team Nate is awesome. They also genuinely care about creator's being fairly compensated.

> Seems like a model could exist for an entrepreneur to create a subscription based licensing program for creators to use music in their streams.

There are a few - I use Pretzel.rocks. (No affiliation.)

Music licensing is already a thing you know.