Aside from the abominable intrusion of privacy this amounts to (because an action is a crime, not a belief of a sympathy)...
I work in security for a large company that uses gmail as its corporate email.
When we receive phishing or malware-containing emails, along with a robust response, we work with our admins to have the emails removed from the mailboxes of the recipients (better safe than relying on every user to not be an idiot.) This is enormously time-consuming, difficult, and all this on what one can only assume is a tiny fraction of over-all gmail. So let's call it impractical.
So where do we go from there? Well, naturally if you'd like better searching capabilities, we should index all the email, all the files. "Pre-search," as it were. I'm sure we'd all be happier with that.
Wait. That's what the NSA was already tasked to do by the US government. And we all lost our shit about it. And for good reason. (And BTW, the NSA, who has a ton of experience and lots of very smart people in this area, never managed to make this terribly illuminating.)