The degree to which copyright is enforced on entertainment websites such as twitch and youtube, specifically in regards to music, has exceeded common sense.
Broadcasters and youtubers are not generating revenue because of the music they play, but the personality, skills, information, and non-music related entertainment they provide. At no point do they attempt to pass the music off as their own - in fact, they often display the names and artists of the songs they are playing. If anything, this kind of exposure generates them additional revenue.
These kind of limitations are not providing any sort of protection for intellectual property, in fact, they are limiting its creation. It's time to re-evaluate the enforcement of these laws.