If your message is unclear or incomplete, it can create a negative impression on your customers when you are away. For example, if your message does not clearly state what dates you will be unavailable, your clients and co-workers are likely to fill up your inbox with messages, making it difficult for you to catch up when you are back. Failure to include the contact information of the person they can contact in your absence can affect your ongoing projects.
I will surely respond to your email when I’m back in the office. But, if this requires an immediate response, please resend any messages that require my immediate attention with a subject line of “URGENT: [Original Subject]”.

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.
About the “overshares”: You linked to a previous column that mentioned this point, “Sometimes the over-sharing of plans can even come across as suspect — similar to how when someone’s calling in sick with genuine illness, they usually just say, ‘I’m going to be out sick,’ but fakers will generally give you a long list of overly specific symptoms, like they feel they have to convince you.”