A one rein stop will only work if you have a large enough safe area to spiral the horse down in and it isn't going so fast that its going to tip up the minute it feels some pressure to one side.
This can only be thought or spoken by someone who has never taught a horse how to stop and give its head like the instructions call for.
The reason I say this is that once you teach a horse to stop and give you its head, it does not spiral down and make circles. You slide your hand down the rein and it simply gathers itself up, does something very similar to a 'half halt' and stops before it brings its head all the way around to your foot.
Every horse I have done this with for over 45 years has learned to do this very quickly in an enclosed area. Then, every one of them has been stopped with one rein this way out in the open a few times and it stays with them. I never had to do the CA stuff of taking their head every time I ride them. I have not found all that 'flexion' necessary unless the horse is a bronc or a runaway. Any time they didn't listen to me and check their speed quickly enough or transition down quickly enough, I would stop them with one rein and it was like, "OK, I'll listen now if you are going to do that."
I had a horse that could gallop for miles across country and over anything that came in front of him if he decided to take off with me. A stronger bit was the only answer to his problem.
This horse would have learned very quickly to listen to you. I have used this method to correct and retrain a number of horses that would 'carry' a person in the hunt field or out on the trail or in a big pasture -- true bolters and runaways. Teaching them to stop and give you their head worked on all of them. It works on 'chargy horses' that get on the muscle.
I have used it on every OTTB for at least the last 35 or 40 years. I was a little Leary of it at first with them. I have used it now on so many of them and on spoiled horses and I has worked so well, that it is the first thing I teach all of them. As I got older and had more arthritis problems (weak hands and a really bad back) and could not argue with a horse, I started teaching it to every horse from the old trail horses to the green babies. It is just like installing an 'off button' and it gets anything's attention back to you no matter what they have started to do wrong. There just are no arguements.
I teach horses to disengage their hind quarters and to do turns on the forehand just so they know how. If a horse is trying to buck me off, you bet I'll get his butt moving when I take his head away from him.
I DO NOT disengage a horse's hind end any other time. I want them to stop and give me their heads with their butts straight behind them. I have found that this does not mess up a hard stop (like a roping horse) or a sliding stop. It also lets me turn a horse's head toward a cow to work parallel to a cow and bend away from the cow by letting me use my 'cow-side leg' and have the horse hold its ground behind and NOT move its butt away from the cow. A horse working parallel to a cow should have a slight arc in its body so it can roll back smoothly toward the cow. A horse working a cow MUST turn its head toward the cow. I usually want that horse to work with both eyes on the cow. He absolutely has to keep his inside hind leg under him and absolutely cannot move his butt out away from the cow when you put the inside leg on him. They have to 'hold their ground'. Teaching them to stop straight an give you their head any time you want it does not foul this up and actually makes it work better.
When ever I read that it won't work for this or that and how it is dangerous or how it can trip a horse or any other stuff, I know for a fact that this person has never taught a horse to do this maneuver from start to finish at all three gaits.