Nooooooooooo. No. No. No.
It's not going to happen and we shouldn't even consider it. Seriously. This thing we are doing here, which is "connecting people to each other," those forces for MANY will be far more powerful than "let me stop and think about the fact that this is forever." I just don't think we are wired for it, we're wired for a world in which we can just talk?
I think it's better to try to engineer some specific counter to "everything is recorded all the time" (or, as in here, not try to usher it into existence even more) than to try to say "welp, everything is recorded all the time, better get used to it."