There are some technical quirks if it is supposed to be a decentralized system but still tied to your telephone number as account identification/address. You'd obviously want to be as independent as possible from your service provider, especially here in Europe, where it is possible to take the phone number with you when changing providers.

It'd probably have to be a system where the server must verify that the number actually belongs to you by sending you a "traditional" SMS with an access code. You'd also need a trust network among the servers or else there would be servers announcing every telephone number out there as theirs.

Regarding the app, I guess any app that supports the protocol would do, even ones that also do other things. This should produce a healty app ecosystem.