Youtube isn't a public space, its a private company that has its own terms and conditions and community guidelines and there is nothing wrong with taking down anything that they feel violates one of their conditions.
In terms of copyright violations, I believe the people who own the copyright have to actually be pro-active in getting content that violates said copyright taken down, which is why some stuff can seemingly go unnoticed and stay up there forever, and other things like certain tv shows keep getting taken down and uploaded again over and over under different account names.
With the sheer number of videos that are uploaded to youtube daily, it was only a matter of time before they needed to extend the number of their staff to review content.