I thought it was funny but could never get away with using something like that at my org. I loved the “competent people who work for me” part – I make this joke all the time. We have some people who feel that they should have a manager personally attend to them and, at least in my case, my highly competent team is in the weeds of that work a lot more and are not rusty (like I am).
Or, worse, when someone has left the organization and the organization hasn’t bothered to put up an OOO, so I’m just emailing a blackhole until I call or someone finally checks that inbox. I never fail to set up my OoO reply, and yet most of my external contacts don’t get them. Let’s say I work for LlamaCombs, with an name(@)llamacombs.com address, and this is a company who has two clients AlpacaBrush and VicunaShampoo. I work primarily with the second, and their internal directory lists my contact info as name(@)vicunashampoo.com. It works because any e-mail sent to the second address is auto-forwarded to the first. Except it messes up OoO replies big time. Because the auto-reply is sent to my own alternate address, not to the original sender, and I have no way to change that.

I worked with a guy years ago who would update his voicemail greeting literally every time he left the office.
Meanwhile, I do sometimes put up long ones when I will be away for some days during a season in which there are a confluence of three or four very likely reasons someone would contact me, and who else they need to contact isn’t the same. Like, it’s high llama grooming season, and generally during this month I get two or three requests per week for each of llama bleaching (for which my backup is Stella), llama shaving (for which it’s Arturo), and llama perming (for which it’s Carter). My message says I’ll be out until blah blah, and if it’s not an urgent llama grooming issue, I’ll get back to you after that, but meanwhile, for urgent llama grooming here’s who to call.