The law is a set of tools commonly used to give people a sense that there is justice and order in our society. When the tools are found inadequate, new ones are developed. Ultimately, this probably won't work in Grooveshark's favor.
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.
https://en.wikipedia.org/wiki/Compulsory_license
If they don't like it, they should change the law, rather than ask the courts to make up new laws for people to follow on the spot.
I realize that there are a lot of lawsuits alleging that, but as far as I know they are all still pending and nothing of the sort has been established in court. That makes your statement premature, at best.
Personally, I put about as much stock those claims as SCO's claims that we should all write them $699 checks for Linux, but we'll find out whenever the courts rule.
Feel free to supply a Pacer link if the situation changes.
There is no compulsory license for sound recordings in any territory for downloads or interactive streaming. You have to explicit permission from the copyright owner to make the recording available for download or interactive streaming, i.e. you can choose when to listen to it.
There is a compulsory license in most territories for the composition side, under certain specific conditions, in which an entity like Grooveshark would obtain a mechanical license for the composition from the copyright holder of the composition (usually music publishers) in advance of its public availability, and then account and pay royalties for its use. This requires Grooveshark to know the songwriters, publishers, and splits of each work, which is not something that comes from the user uploads. It may be the case that their terms of use pass this responsibility to the uploader.
In short, however, you need sets of permission (sound recording and composition) to legally distribute music for download or interactive streaming.