If you give people peer to peer software (such as a web sockets application if the peer to peer part gets implemented, but could be anything) the first step for some kinds of applications is to find a specific person and try to connect with them. If neither of you has a URI (and knows what it is) you need a third party to handle finding each other and verifying your identities. After that the third party isn't needed because you go peer to peer.
I could of course write that third party software and put it up on a website, but then I would have to write that third party software and put it up on a website (or a server that isn't a website if that's how I want to do it).
Does anyone offer this service? Ideally as a website and of course ideally free.