If you don't like it, you can advocate for a change in the law. Frankly, you underrate the difficulty sites like Grooveshark face. Copyright infringement relies upon whether or not a person has permission and that's not something a computer program can determine.
You're using a simple heuristic that doesn't work well at scale, relies upon human judgement (which also doesn't scale), and fails utterly when the marketing departments of these places put out their own leaked versions of things (see Viacom v. YouTube) which are permitted.
It's weird how often I hear how "easy" this is. This is HN. If you want me to believe that it's easy, create a computer program that acts as a filter and we'll see how well it works in the real world. I realize that you see someone getting shafted and want to fix that. That's a good thing. The problem is that you advocate for a solution that would merely shaft someone else instead. That's not a good thing.