If the tire is getting near the end of it's life or I'm leaving on a trip, I'll certainly accelerate replacement if I have a plugged tire. But otherwise, if it's just a simple puncture in the main part of the tread due to a screw, nail, etc., I plug and ride until the tire is worn out. I've NEVER had a problem with a string-type plug. I have had issues with mushroom type plugs and I don't use them anymore.
I've probably had 20 flats in my career, almost always on the rear. I've never had one that felt remotely life-threatening - the bike starts handlying very heavily so I pull over to the shoulder. I do pay a lot of attention to my tires when I service the bike. I've caught many nails and the like sitting in the tire waiting to start leaking. And I pay a lot of attention to how the bike feels and if something doesn't feel right, I'll pull over and check things out - I've caught some slow leakers this way before they've advanced to the point of an outright flat.
The idea that flats are, in general, life-threatening episodes is overblown, IMHO. They happen and you need to be able to deal with them, both with respect to handling the bike during the episode and fixing the bike beside the road.
Whether you immediately beeline to the nearest shop to replace the tire is a personal risk assessment, but given the risks we take on to begin with, I don't find the risk of riding on a plugged tire to be worth worrying about. If you want to be completely safe, you won't get on the bike in the first place.
- Mark