I disagree that these aren't intrinsict to any messaging system. Those are intrinsic problems of any electronic data storage and transfer system. Data tends to deleted or public, as Quinn Norton says.
I've been thinking this problem through for a while, and I'm starting to think we simply need to have a different mindset for thinking of electronic data as for hardcopy. I'm leaning toward "data physics", in the sense that there are different "rules of physics" which apply -- a metaphor, though close enough to the truth:
* Data have effectivley no inertia. They can move anywhere at the speed of light.
* Data violate the principle of location. Information can be in two (or more) places at the same time.
* Data can be exfiltrated without awareness of the subject. Most especially when held on third-party systems.
* Encryption isn't a safe. If you lose a safe key (or combination), you can drill it out. If you lose an encryption key, an entire corpus is no longer accessible. This has absolutely massive implications from a user-support standpoint, as such key loss will be an everyday (or, at global scale, every second) occurrance. Which means some sort of reliable, useful, but still sufficiently safe, and cheap key recovery system.
Essentially: you can be compromised at any time, by any number of actors, without notice. There may be some ways to address this, but throwing more crypto at the problem may not be it. "Canaries" or fictitious entries and sentries (URLs, emails or phone numbers which should never be contacted, but which if they are, you know you've been had), might be part of that.
Another realisation I had a while back was that as much as this hits the ordinary citizen, it's as much a concern for those in or near power (finance, politics, military, journalism, business, etc.) as well. See open speculation that the White House has been compromised, quite possibly by multiple intelligence operators from multiple nation-state, and possibly other, actors. Including those of the United States itself.
Which is to say: media change the societies in which they operate, and always have. Elizabeth Eisenstein made hay with this in her 1979 book The Printing Press as an Agent of Change, though I'm finding her 1968 paper prefacing that work a more concise and sufficient summary of the principles: "Some Conjectures about the Impact of Printing on Western Society and Thought: A Preliminary Report"
http://www.journals.uchicago.edu/doi/pdfplus/10.1086/240164