Where did you get the idea that we need stable addresses? This was solved with DNS, registration protocols, dhts, etc decades ago. Nobody has had stable addresses forever.
stable in the "for the next few minutes" sense, which you do need e.g. for mobile phone or video calls. With mobile phones your address can change every few seconds as you drive on a highway and get passed between cells and even carriers.
DNS never solved this, DHTs didn't either; and I'm not familiar with a DHT that is actually successful except for bittorrent despite many attempts, even for "stable for a few hours" case.
All the cases that sort of work (RTMFP flows, SIP registrations, old Skype, ...) essentially have peer-to-peer communication as a server-offload optimization (that is, peers may talk directly to each other after the server arranged everything iff the stars aligned correctly), not as their main method.
