Who has the hard drive space keeping an up-to-date divx library today? I personnally prefer to download a movie when needed, p2p has become fast enough to be convenient :)
But how hard would it be to create a peer-to-peer internet connection? One of your devices would be connected to WiFi, but also connected to every other device in the area. And those would be connected to more devices, and so on. It would form a big chain, possibly extending several miles.
When someone requests a song, that request is passed from one device to another until it gets back to the device that's connected to WiFi. Then the song data is streamed from the internet and passed back to the original requester.
This system seems like it would be extremely slow. But, does it really matter if it takes an hour to download 10 songs? You could have a list of songs that you'd eventually like to listen to, then check back every few hours to see which ones are ready.
On the plus side, chances are that one of the other devices in your mesh already has a copy of the song you want (especially if it's a popular song) and if storage isn't an issue you can have a lot of locally cached data that should speed things up.
It exists! See for example http://www.fon.com/
By the way, P2P networks don't have to be slow as long as they're well designed; they can even be faster than traditional client/server.