Rubber Manufacturers Association.
Short summary:
All tire shops in the USA follow RMA guidelines (they must, by insurance rules and for legal liability reasons).
No professional would be caught dead using the rope plugs, even as we all know them to work just fine, in practice.
While almost all of us have had continued success with the emergency rope plug, they're forbidden in professional use for a variety of reasons, explained below by the TIA.
The Tire Industry Association decries use of the rope plug here:
Here's their video on the topic:
Having said that, I reiterate we've all successfully fixed dozens of tires with the rope plugs, so all I'm saying is that there is a right way and a wrong way, and both ways have worked for all of us - but the right way is the right way for a reason.
I like doing things the right way, unless I'm stuck on the shoulder of the road, in which case the wrong way is the right way for that situation.
Here's a video of a guy plugging bike tires with a tubeless repair kit:
Take a look at that biker's concept of a "pocket knife" at 53 seconds!
I'm curious if you mount and balance your bike tires? I did that when I owned a bike. It was hard to find a tire shop, nearby anyway, that mounted tires, so I learned how to do that myself. Bike tires are easier than car tires, which themselves are easier than SUV tires (all of which I've done) which are easier than truck tires (which I've never done).
Plugging from the outside is pretty simple on all tires.
Patchplugging from the inside is simple - if - if you have the tools, which cost about $150 and which last forever.