I'd really like to see Twitch implement a system where streamers could upload separate audio channels for their videos. That way a single channel could be muted for infringement without muting the others. You wouldn't have to lose the audio from the game and player commentary, which is often integral to the video, just because a copyrighted song was playing in the background. This is actually a feature that would have some value to me as a user because I often watch streams where I don't like the music but can't turn it off without losing the caster's commentary which often times the best part.

This does put an extra burden on casters but maybe the value of degrading gracefully in the face of copyright complaints will make it worth it.