Streamer mode is typically for one of two usecases:

1. The streamer plays their own music, so being able to silence all game music simplifies things
2. The game might contain copyrighted music by known artists, which can trigger automated enforcement. In most jurisdictions music used in a game is fine to stream/record because it’s covered by the developer’s/distributor’s license, but that doesn’t stop overzealous rights holders from placing bogus claims that can muck up your revenue, so it’s easier to just not play music that you don’t yourself have license to play