I use one rein stop, if necessary, and I always stop the horse with (seat first , of course) one rein more firm than the other, thus encouraging some softness to one side with the jaw. Softness in the jaw helps with softness in the body.
If you teach the stop with just asking the horse to put it's head over to one side and stop, usually the horse is stopping with it;s weight still on it's forehand, kind of like it is hanging over a cliff. you want him to stop softly and to gather his weight back a wee bit over his hind legs. if he stops leaning forward , over his front legs, the second you give him the rein, he will fall forward. in fact, he never really stops, he just "pauses".
he has never GIVEN to the rein through his whole body, he has just broken at the neck, hauled his head to the side, and waited for you to quit this silly stopping and pulling so he can go back to the direction his mind is still fixed on.
So, having him give to the rein AND step under with his hind and disengage is part of teaching a one rein stop, IMO. you wont' always need to go that far, the full disengagement, but you do this to teach him to connect the rein with his "engine" (the hind legs), and to learn to give through his whole body, and not just the neck.