Given the number of questions on this forum, it is certainly something that is asked for. I've noticed that same thing myself.

There are a few systems out there that already try to do this, to varying degree of success. On iPhone, you get it from Game Center. On WIndows Phone, you get it through Live!. On PC, you get it from Steam, if you're integrated to that platform. There are also infrastructure-as-a-service offerings of various kinds, starting with Gamespy and going to places like Gamedonia or Parse.

However, it's not quite as easy as all that. For server listings to really make sense, you need to do NAT punch-through, else users can't get to servers hosted by other users. And, because TCP NAT punch-through is still hit-or-miss (60% success, perhaps,) you really need a UDP-based protocol. And that means you need an entire game networking layer for this to all work out. And when you talk game networking layers, incumbents like enet, RakNet, etc, or built-ins to various platforms (UDK, Unity, etc) have a strong pull on developers.

My conclusion is that the demand is mostly there from those who are just starting out and don't know how to do this, and don't have any funding to pay for a real solution. If you want to create a real solution that will actually be worked by those with funding to pay for it, it's a real, long-term, technology-heavy project, with a significantly long sales cycle and almost enterprise-like scope. Thus, I haven't personally put my time into such a project, even though I've considered it several times.

You may find a different angle to take, in which case, I encourage you to keep posting progress updates, as I'd be very interested in seeing someone taking on this space and succeeding!