Last Summer (2017) ran over a metal boxing staple when we pulled into a steel mill parking lot. (I'm pretty sure that's where I picked it up). Anyway, couple days later, noticed the passenger side, rear tire on the camper was flat.
My next door neighbor, who is a life long farmer, as his father, and his father, he said "no problem". He'd get the tire plugging kit from their shop and plug it for me. Next day he did. Didn't have to take the tire off the trailer or anything. It's been holding just fine ever since.
He told me they plug those $5000 each gigantic tractor and combine tires all the time with plugs. Never had one fail. New holes, but never a failure. The kit he used was brand new, glue was new, plugs were new. I think that makes a difference.
First trip out, I was extremely watchful of the tire. But after a few thousand miles further, I began to relax about it. If it happened again on another tire, I'd do it the same way.
My neighbor also plugged my son's car tire too (he lives with us), when we were on a trip a few days after he did the trailer. My son has had no issues with the plug on his car.
I think tire shops are under a bit more scrutiny than the Average Joe on the street. They do all they can to eliminate liability. So saying they don't don't plug tires, is basically saying, they don't want to take any liability if it doesn't work.
Besides, if the customer buys a new tire for $100, the business is making more profit than charging $7.50 for plugging one!