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.
There’s nothing worse than dreading a return from being away from the desk. After all, you’re likely to have an overflowing email inbox left untended while you were on vacation. Sending out this one email before you go anywhere for an extended period of time will help lessen that feeling.

I had a colleague that managed to set up a rule for an OOO that would only get sent if you cc’d or bcc’d him, which basically said that all those cc mails would get automatically put in a separate folder and he may or may not ever read them – may the odds be ever in your favor basically.
I take advantage of the ability to send different OOO messages to internal or external addresses. Internal addresses get a couple of people to contact if it’s urgent, usually my direct report and my backup person, since between them they can cover pretty much everything I do, or at least they’ll know who can. External addresses get a more general notice: “I am temporarily out of the office. If your message is regarding the Llama Care project and requires a prompt response from our Llama Grooming Team, please make sure that [email protected] is one of the recipients of your message.” Probably not the most elegant phrasing, but we have a distribution list for this very reason. Even requests that they know only I handle are supposed to go to the LG list.