Your idea doesn't sound too difficult to implement but I don't know if people would want to store all these messages locally when the vast majority of people are used to having their shit be stored elsewhere. Additionally, if you wanted to target enterprise users, they would want to likely have all their messages centralised for auditing purposes
I think that's the issue. We're all so used to the idea of free storage and we're not cognizant of the consequences. If we start holding some of our chips in our own hands, all these corporations won't be able to sell us out and abuse us so easily.