All either lack user directory or use phone numbers as identifiers. Finding people through the same instrument is an important functionality, without which a messaging system will not be popular and thus will not be relevant for such situations.

If a messaging system uses SMS for confirmation, then, as you might guess, there is some central point sending out those SMS. So it would have centralized registration. Then technically registration can be disrupted (one can imagine some cryptographic scheme to make this the only disruption). Registration is an important part, even for a popular system many people will not have an existing account when they need it.

User directories - if there is a decentralized user directory listing John Smith, Ivan Ivanov and Obi-Wan Kenobi, then either there will be hundreds of each with no ability to tell which of them is the real one (suppose those names are unique, say, u://jsmith, u://iivanov and u://alongtime ), or you need some kind of registration of public key and nickname pairs. Simplest variant (maybe dumb) is to have the messages telling of such registration having happened to be signed by some “registration authority” or a user delegated (by another message) that right (one would have to trace it to the root sadly). Then, it appears, users may add registration authorities, or choose between them, manually, but then the decentralized user directory would work in some moderated and ordered way.

I’m not aware of any such system existing, and perhaps something about what I wrote is just dumb.