He's not a plant manager. He designs and builds automation systems that do specialty production in factories across the country. He works at a small robotics firm that does very specialized work in a particular type of production, and he is the only one at the company who is an expert this particular type of robotic fabrication. Minor machine problems I'm sure a technician in a factory can handle. Major problems mean they go to him for help.
And no - I'm not saying anyone else is selfish for what they ask their spouse to do on vacation. But I am saying it would be selfish for ME to insist that my husband not work on vacation. The last vacation we went on he was able to fix a programming issue remotely while we were at a resort in Jamaica. Had he not done it, that line would have shut down for a full week, a bunch of hourly workers wouldn't have made their salary that week, and a specialized type of medical supply (that some people need to live) would have had a shortage for a couple of weeks until the production line got caught up. I can't imagine asking him not to do that.
I don't doubt that he is the expert on a given skill. But if he is truly the only one that can address major problems, then the company needs to do an enormous amount of additional training for their other employees, or hire another person. The "win the lottery" scenario is real, and any successful company needs to be prepared for it.