I picked up two punctures last year on my Michelin pilot pure rear, got given the usual tosh by a few tyre dealers when phoning around that nobody repairs Z rated tyres! but did find a couple of fitters who do and the official line is that they can be repaired but can't be guaranteed like the lesser rated tyres
Dunlop say on their website that repairing a z rated Tyre is okay as long as the hole is under certain size And within a couple if inches of the centre line.
I had 3 at the end of last year... Brand new rear cuz it could not be plugged - picked up an allen key!!!! then my front a bit later on, then the rear again, but I was able to plug the rear. I can't help but ride in the dirty bits, it's the only way to get to the front at the red lights!!! I actually pulled my bike out on Monday to go to work, and there was a MASSIVE chunk of metal in the tyre the size of a big beetle... I had to pull it out cuz if I rode like that it would puncture anyway!!! and luckily it did not puncture the carcass... whew!! Plugs are fine. There has been a plug in my rear for the past 3,000 miles, no probs. Actually, you should not plug a front tyre, is my understanding... And when the road is wet, tyres puncture easier, as the offensive object is slippy...
I havent used a plug yet, always have used patches but I do carry a plug kit with me.just always managed to pick up slow leaks so far.
Totally agree that having the tyre professionally repaired shouldn't be an issue. I have used the emergancy plugs but thought these weren't permanent? I always get it repaired after by a professional tyre place.