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.
I can see the value in the distributed part certainly but if the storage requirements are very large due to a large volume of messages (I'd imagine any solution which caught on could quickly outpace the number of transactions on something like the ethereum or btc network), wouldn't it necessarily just end up centralized?
It's an interesting idea though.
Well https://tox.chat and https://ring.cx (now Jami) can do just that as well as https://briarproject.org.
So these do exist. Such a thing was also being proposed for Ricochet https://github.com/ricochet-im/ricochet/issues/54