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.
This is not likely to be the case.
Sure, but that could be up to every sender to decide whether they want their messages to be view once/view for 24hrs/store forever.
Secure messages shouldn’t persist and if they do they aren’t secure. Being able to export, upload, and restore an entire conversation history is the opposite of secure.
There is no point in using a secure messaging system if your entire conversation history can be downloaded the minute a single person in your group loses physical security on their device. Just use FB Messenger.