Copyright law is complex and nuanced. Systems like YouTube's and now Twitch's are simple and blunt, and are fundamentally incapable of effectively doing what they're meant to do.
Ustream ran into that when it broadcast the Hugo awards two years ago; its own "protection" system kicked in and killed the live stream because the show, like every awards show, included clips of an award winner... which were detected as copyrighted and blunt-object smacked off the internet because the system can only detect matching signatures, and lacks the ability to recognize matching unlicensed non-fairly-used signatures.
There are already reports coming in of videos being muted on Twitch because the built-in, licensed soundtrack of the game itself is audible in videos of someone playing the game, and it seems from another comment in this thread[1] that one of Twitch's own official broadcasts got muted because the system could only recognize "copyrighted", not "copyrighted and used legally".
This is a doomed project, and it could doom Twitch, and if you really do care about artists being compensated, you should not be in favor of things which make that cause seem so odious and stupid.
1) Often certain music is played simply as a "cultural reference" -- e.g. making fun of it, having it in the background shortly for dramatic or comical effect, and so on. I would think most classify as fair use; however removals will likely be irrevocable and done with parsimony.
2) Even if the broadcaster would like to give up some of his revenue for copyright, he won't be able to. It just doesn't make much economic sense for large brands to issue small licenses, yet it does make sense to go after small violators since they're allowed to do it en masse.
The point is, viewers lose culturally and copyright holders don't actually gain anything.
Chariots of Fire https://www.youtube.com/watch?v=TYJzcUvS_NU
Wagner's March of the Valkyries https://www.youtube.com/watch?v=XRU1AJsXN1g
Gonna Fly Now https://www.youtube.com/watch?v=cyvQKTg4T5o
You can't really replace those.
I hope that the policing of mainstream commercial music use will drive content creators to use music owned by small companies and independents. Twitch should do an integration with Bandcamp or something.