I think the most important thing is to focus more on the professionally-made material while letting amateur videos made for fun remain on YouTube. Removing home videos with songs playing in the background is nonsense to me.
This reminds me of when I was in school for graphic design. We were told to change an image in seven distinct ways before using it in our work. I am not sure if there is any legal merit to that, but it is a good way to scare people out of using other people's work.
I'm not sure where the line should be drawn. Copyright laws should be frequently reviewed and updated to keep up with the rapidly-changing means of creating, using and sharing media.