Going back to how some people can’t ever switch off, this person went above and beyond for their auto-email with a humorous graph that very accurately shows the highs and lows of stress levels before, during and after time away.
Most awkward/painful one I ever saw was a former co-worker. ~10 years ago when he left on paternity leave, he said as much in his out of office. The baby was stillborn. It stayed up for the month or so until he returned. Those of us in the same office of course knew the situation, but we regularly communicated directly with multiple offices in different states and countries. The very first time I saw it I was overcome with dread about how many congratulations he would receive and have to tell the story to. I was much younger and afraid to rock the boat then, but I think now I would push his manager and IT to use their ability to access his account and change it.

I just say “following my return to the office” because saying “as soon as possible” isn’t actually when I’m going to respond — I may have other priorities when I get back that take precedence over responding to a week old email that wasn’t important enough for them to contact my backup. That said, it doesn’t bother me when other people do it!
I think the problem is that “at your earliest convenience” is a formulaic convention that uses explicit, almost exaggerated politeness to basically issue a stern direction, meaning “as soon as you possibly can”. When you turn it into “at my earliest convenience” it’s unclear if you mean “whenever it’s convenient for me to get to it” (what the words say) or “as soon as I possibly can” (what the meaning of the formulaic original is). Or else it sounds like you didn’t quite understand how “at your earliest convenience” works.