I used to work with someone who had a message telling people she only checked her email twice a day. You pretty much needed to call her if you needed anything outside of those times. (She worked in a remote office.) I think she had read one of those books on efficiency that recommended scheduled email time. But there were problems with this: 4. My department often had to email attachments or text to illustrate our questions/concerns. And we were on deadlines. Reading a page of text over the phone was not an efficient use of anyone’s time 5. She did outreach & was often out of the office on site visits, trainings, or travel to these places, but never ever set her OOO for these, because she was “working.” However, she was effectively not available to read emails from other staff until after hours on those days.
After all, your goal is always to keep your business associates happy. For that reason, you should have a backup co-worker who will cover some of your work while you are not available. Not only is this the professional way to go, but it will also leave your customer satisfied with the company’s service.

Thank you for your email. I’m out of the office and into the cookies and eggnog right now. I’m celebrating the holidays with my loved ones and will not be checking my email until [return date].
Company President doesn’t want sales to use ‘out-of-office’; they’d prefer that the customer feel we were always available for them – 24/7. They also say that vacation are just nicer places to read emails….