Our legal system might be based on UK law but our product legislation and most consummer laws come directly from the USA right down to having footpaths called sidewalks in a lot of them .
So usually if we make something illegal down here it is because you made it illegal over there. Or at least one state and we seem to idolise Californian legislation .
We have 3 separate bodies that do product law and none of them have the faintest idea about the products they are dealing with if some one in the USA mounts a successfull case against a tyre shop , we ban the practice.
And if it is dangerious for car tyres then of course it must be dangerios for all tyres so it gets banned right across the entire industry.
And no mower tyres do not blow out, lazy typist .
They do roll the bead off the seat and instantly go flat which has the same nett effect.
Risk assment managers do not look at what actually dose happen they live in that strange world of what could possibly happen.
They advize civil servants with no practical experience who draft regulations to protect the country from their own fantasies and if no one dies from having a deflated ( blown was easier to type ) tyre then they have done their job so deserve their bonuses.
And no I litttle idea of which level of government actually dose what jobs apart from what I hear in seminars, & in docummentries etc hense the / between state & federal.
As for the mechanics, mower / off road tyre plugs take quite well to sidewalls, substantially better success rate than with car tread plugs as they are softer & stickier
But all this is twaddle, the OP was just wondering why the tyre shops would not install a plug, perhaps you might be kind enough to verify the legality of tyre plugging with your local tyre shop.
I could be totally wrong and if so would greatly appreciate being corrected.
Having a science / engineering back ground I am always happy to be proven wrong which is one mechanism of learning what is right.
This being an open forum and existing forever is cyberspace is is good to have the currently correct information in it.
FWIW I only fit Safety Seal brand plugswhich are a lot more expensive than any thing I could by from the cheap and nasty made is China discount shops and to date have never had a failure.
AFAIK they were actually formulated for 4WD use and found to work well on mowers. They are the only brand stocked by my 3 wholesalers, all of whome sell other products from oher companies that make plugs but none of them stock those plugs.