Here’s my pet peeve: OOOs that specifically state the person “won’t have access to email.” It contributes to this pervasive idea that an employee who might technically be ABLE to check her work email while OOO better have a damn good reason why she won’t be doing so. Which calls back to the reason someone’s OOO is no one else’s business. Whether you’re OOO because you’re on your honeymoon, having your gall bladder removed, or robbing a bank, OOO should automatically imply unavailability for work stuff. Full stop.
According to American Express, “Six in ten customers feel that companies meet their service expectations”. Customers look for faster resolution and rely on the expectations that businesses set with queue time for evaluating their service quality.

That doesn’t sound odd to me at all, depending on the company. I used to send a staff-wide note because they needed to know I would be out and they could plan accordingly if they needed anything. At my current company I wouldn’t do this, but that’s because it’s massive and I only directly work with a small team.
For many roles, of course, the sort of OoO described wouldn’t work. But there are a lot of roles where people would survive just fine letting their requests sit for an extra week before forwarding again. And especially at smaller companies where there they might be pressed for coverage when people are out, I think it’s great to normalise that a job is basically ‘off-line’ for a week or two so that the employee can rest and recharge.