Now, the focus here should not be on protecting Youtube from all international copyright laws - the focus should be on protecting its users from them. Allow me to explain:
A few posts above me, someone mentioned a certain aspect of the law called Fair Use. This is an important term that everyone should become familiar with, because it is this term that will ultimately be the battleground for your rights on the internet for the years to come.
Riddle me this: What is the difference between Siskel and Ebert reviewing a film on national television, and the Nostalgia Critic reviewing a film on the internet? There is none. Both are known by the same name - transformative works. A transformative work is any original content that is made by using the original content of another entity within the realm of Fair Use law.
Now, one would think that this same principle would apply to Youtube, correct? Well, I'm afraid that just isn't the case. You see, Youtube is run by Google, a company that has been known in the past to loathe legal battles to a great extent. Youtube's copyright reporting system reflects this - they rely on the "honor system", meaning you can use the reporting system to operate under the guise of any company you want, and take down a video under copyright infringement, with absolutely no one screening these reports. Instead, Youtube uses an automated entity of some sort to act on these reports. This way, they avoid any and all legal battles no matter what.
Technically, this is breaking the law.
Here's an example: remember not too long ago when WMG sweeped across Youtube, taking down or muting any and all videos that contained a music track with even a few seconds of their music? That was (in most cases, not all) breaking the law. Many of these videos they took down or muted contained this music, yes, but it fell under Fair Use law - they were original content videos, but contained the music created by another entity.
What of the videos containing gameplay footage? They're (in most cases) transformative works - reviews, satire, and the like. And yes, even Let's Plays fall under Fair Use. Why do you think Unskippable can exist? It's a video series here COMPLETELY DEDICATED to showing the cutscenes of games. It's okay though - it is a transformative work.
Look, the point I'm trying to make here is that videos containing just a song, or just an episode of a TV show, or just a cutscene of a game are wrong - They SHOULD be taken down, because they DO infringe on copyrighted materials. However, most of these videos that are taken down every day are not like that - they are protected by the law, and the law is turning a blind eye. Nothing needs to be EXEMPTED from copyright - rather, the laws surrounding copyrights need to be ENFORCED.
TL;DR: No - just enforce Fair Use LAW, and we'll be fine.