OK, but then how do you choose that deadline? If you don't hear back by then, fundamentally you are still taking a destructive action without any positive verification that the original request to do so was legitimate, which is still likely to be a bad experience for the real customer if you've been fooled by someone else.
I'm struggling to think of a situation when I'd want to follow that email-with-deadline pattern but didn't intend to complete the destructive action anyway, like closing all accounts because the service is shutting down, or notifying customers that you're changing business model and they need to switch to some alternative under your new terms first if they want to continue using your service.