I worked in a call center for Big-Evil-Bank for five years, and every new manager would have a different OOO policy/pet peeve that they would require phone-miners to follow. In particular, the memory of the six month period where we were forced to put an OOO up if we left our desk for so much as ONE HOUR smacked me in the face when I saw question. That was by far the worst/strangest/most tedious OOO policy I have ever been forced to follow.
Huh. This is a rare column from you that I disagree with almost entirely. I guess to start with what I think you get right, there's no need to apologize for being out of office, and no one should feel obligated to deal with anything other than a legitimate emergency (which are, in most fields, truly rare) while on vacation or while taking time off.

This would go over like a lead balloon at my company, and, were that person on my team, I’d tell them to change it. It does have a connotation of “when I feel like it” about it, and most of my team is not high enough up the food chain to take that sort of stance (and the ones who are high enough up are client-facing and have the good sense not to do so).
I’ve run into the “no voicemail” thing at a few businesses where phone was the main mode of contact too, and it was hugely frustrating. You call your doctor to ask about, say, a billing issue, and it turns out they’re closed, but then it just says the office hours and “goodbye *click*”. Seriously? Sorry, /end rant.