I do this when I’m on personal vacations. When I’m doing field work for research, I do tend to add a statement that I won’t have access to email/phone because I’m doing field work in X location.
I find it rude, as well. If someone is emailing you (the royal you), it’s because they need something. Saying you’re just going to delete it without also giving that person a Plan B contact is totally rude. It sucks having to go through emails, it does. But it’s part of the job. In my role, I get requests from internal colleagues and from external partners. Even though I provide those partners with an alternate email to send their requests, it’s still my responsibility to make sure that the requests that were sent to me in my absence were handled. Saying “everything I’m sent will be deleted” just Would Not Fly in my industry.

Who talks like that? A blowhard, that’s who… I promise, gentle customer, you won’t hear garbage like that from me. I’ll tell you why I like Aviation… Because it tastes like somebody finally made a gin for everyone.
So, for whatever reason you’re out of the office, your email inbox should be informative with any information about office closures or unexpected absences: Include an expected return date and time. Offer alternative point of contact and their details. Add the general office contact number and email address if you don’t have a specific point of contact. Be friendly and warm in your tone, even if you choose to keep it simple.