depends what your users' interests are. if they genuinely want the site to only offer legal music, then sure it might work. but if most of your users are using the site as a free streaming service, it's not in their interest to remove music that they like.
About copyright, why not make it difficult to find protected music? If people share their own content, the name of this file will not be named as a Justin Bieber song. It will be your own name. I believe most sites want to share protected music and then try to negotiate their use.
Eventually, people may try to game the system, but the site may have an automatic way to freeze the song after receiving a complaint and check if it is a copyright infringement. And this file can be used to feed the system, so it can avoid futures complaints.
I basically wanted to build what SoundCloud was in its early days, before they lost touch with their user base.
The other main point about the copyright infringement in the article wasn't on my radar at all, because I wanted my site to be for music creators to share ideas and collaborate, rather than post commercial music on - but thinking back, THAT could have become a huge problem too, if, as you have suggested, nefarious people had simply used my platform to share non public domain music.
NB: I use SoundCloud to share my own recordings and song ideas, and to listen to other people's ideas and do collaborations with them. NOT to listen to mainstream music or podcasts. I wanted my clone service to facilitate that.
Which is why I had never really factored in copyright violations. But I am thinking as well as human moderation, couldn't such a service also employe a HackerNews style voting system - basically if a song started getting flagged by users as 'copyright violation', it would start to disappear down any searches or catalogues, until enough votes caused it to disappear from the service altogether?