Maybe it's necessary to move in that direction (and maybe emails stick around only if you've specifically flagged them?), but you're going to have to drag people kicking and screaming into that kind of system. Gmail search has spoiled us.
That may mean transcribing instructions into a stand-alone checklist, writing up formal user stories, or the like. However, those acts also clear away a lot of cruft that can otherwise make it nigh-impossible to find the needed info. I've run many a Gmail search, only to find that a valuable email was buried under innumerable "Not quite what I wanted" ones.
I'm not even sure current e-mail systems are such a good tool. I would think chat for internal things and some CRM type system (leveraging e-mail) would be better. But yes as you said, easier said than done.
What you describe is "I want less company security, more personal convenience". (As almost everyone wants, almost all the time).
Worth it to avoid something like Sony's indecent? Probably. Easy to convince the non-technical decisionmakers of that? I'd bet not.