WebRTC makes it possible, but not easy, nor abstracted. You still have very long connection strings to establish the connection, and those strings change as you move around, so it's not something we'd want to ask users to send to each other in order to establish a connection. The approach usually used is a server where the two people rendezvous to exchange the connection strings. That server is kind of like what we have – but then once it's in place, changing over to WebRTC just doesn't seem as exciting. (And even then the connections are slower to establish and less reliable than WebSockets.)

AFAIK WebRTC just works with the latest Firefox/Chrome and needs a STUN and/or a TURN server.