Few things...in the example video for this post, the British rapper mentions Fair Use and in the post Cory also mentions PRS which is also a UK rights collection agency. There is no such "right" as fair use in the UK...fair use is a US concept of law...a common misconception.
And this isn't an issue with the law not working but a simple fact that when platforms like YouTube were created, they never took into consideration issues like Copyright so they never had anything in place to provide protections against infringement or a proper way to avoid these issues...it became an afterthought and something that has been slapped on. YouTube simply grew too fast and as we've seen in court documents, they actually encouraged a lot of infringement because they knew it would push their growth numbers. Google inherited this problem when they acquired the company. That's the problem...everyone is dealing with copyright as an afterthought.
Copyright actually is one of the only protections that indie artists have to protect their own work and again...this isn't so much an issue that the law can't keep up with technology, but that technology never stopped to think about how to work with the law. Almost all of these services was built on infringement and while it has great promotional potential for upcoming artists, it also responsible for an enormous amount of infringement that has cost artists, not simply major labels, a lot of money. I know artists personally who have millions of dollars in lost revenue sitting on YouTube...and they don't bother to fight it because they a) don't want to come down on their fans and b) can't afford to spend the time fighting every video. But Google still gets paid for that infringement. So this really goes both ways.
Now people here keep saying, time to launch "indietube." Well that's a cute suggestion, but if you think whatever you launch won't need a licensing deal with rights owners, you are sadly mistaken. Anything you start will be in violation of copyright if it uses works from others...even if they are derivative or you believe they fall into "fair use" territory, because of course, fair use is a terrible protection under US law. Now I'm not saying that there shouldn't be something like fair use, but the problem is it is so ambiguous that there's no clear cut way to really protect works that doesn't then involve lawyers and courts to interpret what is fair use. It's a bit like the Supreme Court justice statement saying they can't define pornography, but they know it when they see it. The other problem of course is that your average person doesn't understand copyright at all...most people only believe myths around copyright...and of course if you wanted to do the right thing and get a license...that's nearly impossible. That needs to be fixed.
The actual solution to this problem is to rethink, not copyright, but infringement and build a licensing scheme that allows anyone to take anything they want and create something new, that has the full permission of the rights holder...and that ensures the rights holder gets something for their work. If you make money from someone else's work, they deserve a cut...that's only fair.
One last comment...someone mentioned above that even with permission from the "game company" their LP videos were taken down. Of course they were, the gaming company doesn't own the music...they license it as well and they can't give you permission to use the music. They don't have that right. They aren't allowed to grant you a license.
Again...the problems inherent in the system aren't because artists want to protect their work or rights holders are enforcing copyright...it's because the system isn't set up to "allow" creation...only enforce copyright...this is the fundamental change needed in the system around the globe is the ability to grant rights so that the act of enforcing becomes the minority issue for true infringement.