We’re in the eventing forum so this probably isn’t applicable to most of us, but my counter to this would be, how many of those English riding instructors actually take themselves or their students out into open spaces where they’re at a greater risk if a horse takes off and consequently need to know a one-rein stop/pully rein?
I learned this pretty much as soon as I started having XC lessons over tiny logs out in the back field at my lesson barn when I was a kid, because my trainer definitely wasn’t risking it (even though I was on an absolute dead-head QH). I also know more than one trainer who is terrified to let their lesson students outside the walls of an arena (probably because they themselves are terrified to go outside the walls of an arena), so they definitely aren’t teaching it.