Besides, the only thing that really makes riding safer in the end is how well your "brake" cue is established, whatever that cue is. No physical device can make up for that I'm afraid.
Indeed. If I had to rely on the physical severity of the tack in order to be able to brake, this would be a clear indication that I have to go several steps back in my training. If my horses chose not to stop when I was asking for it, my choice would be to
(1) Make sure they understand what I am asking, even if I am not giving the perfect seat cue in that situation for whatever reason. I do this by establishing a stop signal that they always understand - for me that's an audible breathing out for example. At the same time, I would work on my regular stop cue and reward for any reaction to it, so that in a situation where the horse is not quite sure what to do, stopping will be his very first idea, simply becaue it has become an overlearned, automatic reaction to my cue.
(2) Make sure that I am not getting them into situations where they feel too overwhelmed to respond to me.
For me personally, if I had a bridle to which the horse reacted although he decided to ignore a simple halter in the same situation, this alone would be a reason to be very wary of using that bridle. I find it way too scary to rely on the ability to "make the horse stop" with a mechanical device. For me, those devices are not meant to be about control but as a support in our communication. But I don't see them as a substitute for that communication.