I can't say I have ever "taught" a horse to do a one rein stop.
I do, however, teach the horse to bend and give their head in both directions, and to move every piece of their body.
In the last 2 years, I can only recall actually using a one rein emergency stop 2 or 3 times. Once was on a colt to stop his bucking fit, and the other two times were on my gelding when he bolted out of fear (we've resolved that issue).
I personally feel like if you take the time to train your horse effectively and also do plenty of ground work to earn their respect and trust, then you probably will never need a one rein stop. No, it doesn't mean that emergencies don't happen and that "bombproof" horses can't explode, but taking the time to give your horse the tools ahead of time can make a world of difference.
That being said, I never do a one rein stop as a "normal" stop, because I"ve trained my horses to stop normal! (like they should)
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.