I agree that self-plugged repairs should only be a temporary fix until a proper professional repair including a patch can be performed (especially when you consider there could be unseen damage on the inside of the tire), however, I too have driven lots of miles on self-plugged tires without later getting a proper repair. I’ve had mixed results with string plugs - some repairs lasted indefinitely, others leaked after a time and needed to be replaced. Often, even a successful installation first required a couple of tries as releasing the plug properly from the insertion tool wasn’t successful on the first try.
In recent years I’ve switched to a rubber mushroom-headed plug system marketed by Stop & Go (they offer several systems including string plugs). The insertion method is ingenious:
(1) Ream the hole using probe (looks like an awl) and reamer tools like in other systems.
(2) Insert a (silicone) pre-lubricated rubber mushroom-headed plug in one end of a special machined plugging tool (looks like a small impact driver), and fully seat the plug using the tip of a nozzle (looks like a funnel). Set the plugging tool aside.
(3) Screw the nozzle into the awl/probe, then insert it into the hole in the tire. Push while twisting until the nozzle tip is fully inserted into the hole in the tire.
(4) Unscrew the awl leaving the nozzle in place.
(5) Screw the plugging tool into the nozzle in the tire.
(6) Place the provided hex key in the other end of the plugging tool and turn clockwise until it bottoms out, at which point the plug has been pushed through the nozzle into the tire, with the mushroom head protruding on the inside of the tire.
(7) Remove the hex key, and slowly pull the plugging tool away from the tire leaving only the plug’s stem visibly protruding from the tire.
(8) Pull on the stem a bit with a pair of pliers to fully seat the mushroom head on the inside of the tire, and in its rest state, cut off the excess stem with a small blade, also provided.
(9) Place the hex key back on the end of the plugging tool and screw counterclockwise until it stops to prepare the tool for a future repair.
The Stop & Go Pocket Tire Plugger (Model #1000) includes everything but the pliers in a small zipped vinyl pouch along with pictured instructions on a laminated card so you can even read them in the rain. The system is very compact as it was originally designed for tubeless motorcycle tires, and some kits also come with CO2 cartridges to inflate those tires. The procedure sounds lengthy and complicated but if you watch their demo video (https://www.youtube.com/watch?v=vCVNRtmxHEs), it is easy and intuitive. All you need is the kit, a small pair of pliers (if you don’t carry a multitool), and a dependable 12V air compressor (preferably one with a cooling fan to keep it from overheating and seizing) and you’re good to go. I have these in all my vehicles.