YouTube vs. Warner Music

I understand that copyright is an important thing for music and even artworks itself. But since YouTube is a public website, and anyone could sign up for it, I think that people should not have to take down their video unless it is not appropriate for the public eye. Most of the users of YouTube are usually amateur, and they post up video for fun to share with friends and family. I feel that the Warner Music Group should not have had YouTube to tell the high school sophomore to take down her video, in a way it is her own version of the song. If every song is copyrighted, which it probably is, so people can’t just sing for fun, like in karaoke or other. What about American idol or America’s got talent, the contestant all sing already known songs. Even though if you tube ask everyone to take down their video because it was copyrighted, there will be other websites that will post up. The corporations will have to track down every websites. I just feel that to keep both sides happy, maybe the users should add on the artist and title of the song, so that they are not “stealing” the song, they mentioned it.