At my old job, you used to nominate a contact for when you were out of the office and there wasn’t an obvious person to contact. One department was so small that they all just put the all team email so they never had to change it. Trouble is, it turns out Outlook team emails by default only accept internal messages :X
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.

Sample Phone Scripts. After Hours Voicemail for a Small Business: Thanks for calling (our company). The office is currently closed. Office hours are 9am to 6pm, Eastern Time. Please leave a message at the tone and we'll call you back on the next business day. Thank you. Voicemail Script: You have reached (your business name).
I’ll be at a work off-site and will have limited availability by phone and email until ___, please contact ___ for immediate needs about ____ otherwise I will respond as soon as possible”