This is a pretty good idea to implement for security in general, but isn't it a pretty exhausting amount of work just to avoid confrontation with a single person?

You could just put a lawyer in the mix, and make the employee sign a document that ensures all PII has been destroyed at time of firing, with a little more severance for the indignity of it all and clear consequences for non-compliance. If they're not an idiot, they'll do it