This is a nice, but ultimately utopic, non-sensical, impossible security requirement. I take your point that anything persistent is insecure, but anything received is potentially persistent.

There's no such thing as perfect security, there are only levels. Even a system with some hypothetical form of perfect plausible deniability designed into the receiving end could be compromised via transit metadata.

Saying persistence makes secure messaging pointless is pure hyperbole. Encryption protects against a broad range of threat vectors, some simple, others extremely challenging. There's value in every measure.