Agreed. I think some people don’t analyze the individual words when they hear the phrase. It’s fine to say “please let me know at YOUR earliest convenience” but it’s weird to say “I’ll get back to you at MY earliest convenience.”
Yeah, announcing you were going to delete emails unread and expecting the sender to resend when you return would NEVER fly in my office. I’d get executive complaints about that, especially if it went to a client or outside party – if a client can’t reach you, they will reach out to someone else who may not work at your organization and you lose business. I feel like this delete-it-all philosophy would only work for an entirely internal role where timelines are more relaxed, and even then, I feel it’s a bit unprofessional to foist your own catch-up work onto others, especially if they’ve been backfilling for you while you were OOO.

I’ll be 1 percent connected while on vacation so I’m not 100 percent panicked on return. Thank you for emailing me.
I am the LW! It’s interesting, having Alison type out the OOO reply comes across less condescending than how it did in video. I’m sure it works for their office but it also says a lot, potentially, about their culture that she’d need to write something out like that in the first place! Usually “I’m OOO from X to X, please contact X for (reason)” should suffice.