Advertisers and Sponsors Pay Copyright royalties.
Why not get together with the Msuic and Movie copyright managment companies ans such, so that you can work out an agreement that allows copyright owners to be paid, and Twitch isns't being sued and spending tons in that effort.
This would pave the way for people to be able to use music, and show things without violation of copyrights. At no time should broadcasters/streamers be given any of that revenue. Why? Simple, the content is not owned by them.
If you can have systems monitor for violations, just set them to place links within the video, and in the descripotion of the video as well. These would link to say AMAZON legit places to buy the content being used.
In effect instead of it being a negative, use the fact people like the content enough listen to it ir show it as free advertisment for the links that allow others whom may be hearing or seeing something for the first time.
I get this will be a huge undertaking, and that copyrights are very complex in many cases. However, what is less complex is the fact you can turn a chash poor situation into a very profitable one, and provide another benefit/feature for people to broadcast and chillax on Twitch.
Let the companies whom wish to profit off of the userbase here cover these expenses.
AbiliTV on Twitch