A client rings to tell you your out-of-office message has a typo in it, or, worse, is mind-numbingly boring. Suddenly you’re wrenched out of holiday mode and back into the throes of work, weeping as you log back into your email server to change your response as your shandy grows warm and flat.
Well, but as others have pointed out, that depends on the part-time job and the industry. If you don’t work Tuesdays and Thursdays, but those are considered standard hours in your business, clients or other folks outside the office might email you on Tuesday morning with something important, not hear back and not know why — and get irritated. If they get an OOO, they now know what to expect or they have a backup option if the matter is urgent.

Ugh, I wouldn’t mind changing daily if I could have a couple of prepared responses for normal circumstances (i.e.: “I’ve left for the day, but I’ll be back in the office tomorrow morning to return your call”) to select from, but having to create a new message for Tuesday night when the info for Monday night is the same? Rage inducing. Email is asynchronous, you KNOW you’re not going to get an instant reply and sometimes you email knowing fully well that it won’t be seen until the next morning/week/whatever. Why on earth mandate an auto-reply for that?
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.