Again, this will depend HUGELY on what sort of role it is (an external-facing vendor, for example, should probably not use something like this). But for many internal requests, it is not power-tripping to ask someone to either redirect their email or wait until a later date to send it.
Thank you for your message. I will be out of the office starting [start date] and returning [return date]. While I am [reason for absence], I will have limited email access.

You don’t have to stop using OOO messages. Instead, they need to be used wisely. It’s okay to suggest an alternate contact while you are unavailable or add a date when you will be back in action. Just skip the details about why you set up the out of office message. No one needs to know that your son is getting married in Paris. Remove any personal details in that message, including personal cell phone numbers or an alternate email where you can temporarily be reached.
Here’s my OOO nightmare: when I was a graduate intern a few years ago, there was a volunteer with severe, marginally treated mental health concerns. Her behavior toward me was inappropriate to the point that my school assisted me with a safety plan. I obviously blocked her on everything I could think of. Unfortunately while I was on winter break she emailed my agency address from an account no one knew about, got my OOO message, assumed it meant I was open to communicating again, and proceeded to have a monthlong meltdown in my inbox when I didn’t respond. To this day I am grateful for my city’s utter lack of public transit, which prevented her from trying to find my home and family.