I think it is more of a mental condition than a physical hardness, a horse that has learned to ignore pointless pulling. It just becomes like white noise.
If the rider pulls all the time, either from poor balance, or because they are fighting ineffectively with a horse, the horse will just learn to ignore and pull against it.
In that, the horse does learn to travel tense in the jaw and neck, so he is actually less receptive to being supple to light cues. Riders fix it temporarily by upping the bit to a harsher one the horse can't pull against, but if they don't get their hands quiet, and they don't learn to give the horse a place to escape pressure, the horse will learn to take that too and they end up just upping the bit again.
I ride with an egg-butt snaffle on Bay. About the mildest bit there is. He's been ridden in harsher before, and he certainly can get strong on me. When he does that, when any horse does that, my answer is to stop, relax my hands, relax the horse through some bending work like a circle, or slow down, release the rein on them and then slowly collect him again again with the lighter hand. You can't relax them out of a tugging match.
I can manage Bay in this snaffle because I can get him back through seat and hands.... if ecurbh was gonna use him on trail I was gonna switch him to a mechanical hackamore because in a runaway situation, simply pulling on a snaffle is not going to win.
I've always ridden in a mild curb. I think it's just a given in gaited horse circles. May be something about the head set, I don't know. I tried a snaffle for a little while but always felt like I didn't have any brakes so I went back to what I was comfortable with. One of these days I'm going to try it again. I'm not riding with such a fast crowd anymore so it might work out.
I use a Herm Springer snaffle on Tuffy but he gets wise to it after a while and starts lugging on it. I switch to a curb bit with a sweetwater mouthpiece (super mild curb) when he gets spoiled, use it for awhile, then switch back to the snaffle.
Your idea is better but I always ride on a loose rein and there is really no excuse for Tuffy to lug on the bit. He's just being the spoiled brat that I've taught him to be.
I just got something new that I'm going to try. It's a Darnall Billy Allen snaffle and I put a mecate on it. Someday it's going to dry up and I'll get to use it.