I imagine a high quality plumbing company requires someone inspect the quality of work, discussing with potential clients in person, and other such non desk work. Perhaps even getting one’s own hands “dirty”.

This is what the three people I have known that owned umbing companies did. They had someone they paid to handle a lot of the simple repetitive computer stuff (probably could even automate a lot of that now but I don't think they were people who would have though about that) and they would hop to different current job sites to check on work being done, check in with contractors to make sure work is good and employees are good, go to potential new job sites to meet with contractors or home owners, etc.

Yep.

Spent a summer working in a blue collar fashion for a small company. It was fun-ish, but the owner was at a desk all day.

Actually, it does still involve lots of on your feet work. The owner is more often going between current sites to check work that's being done, going to new potential sites to talk with contractors and/or potential customers, etc. Yes, they also are handling the business end but for a plumbing company that doesn't mean you are at a computer all day, there isnt enough atuff for you yo donin that aspext to keep you busy.