Almost everything is covered by copyright, it's indeed not too hard to figure out if something is covered by copyright. It's much harder to figure out who owns the copyright on something, and it's almost impossible to figure out if a certain file is authorized by the copyright owner.
Just because a file is popular doesn't mean it's infringing. Can you guarantee this popular file wasn't posted on twitter by the artist for a marketing campaign? Can you guarantee the artist didn't upload it to a torrent site to get attention? No, you can't. You'll just take a flamethrower approach and many legitimate files will be removed in the process.