There are plenty of non-blockchain approaches to persistence as well which also fall under either the "distributed" or "p2p" labels.
The part I'm having a hard time with is that blockchain's specific strength relative to other distributed approaches is the ledger. That's not really the crux of the decentralized messaging problem.
Unless you need the immutable ledger, other approaches solve identity, privacy, and persistence aspects of messaging just as well or better without the overhead that blockchain approaches introduce.