^I don't believe it's a good move to punish/discipline/put further pressure on(whatever you want to call it or specifically use) a fear reaction. I don't think it's fair or generally effective. And the horse is effectively already being 'punished' by being in that situation. The exception would be in 'emergency' type situations, when the horse's attitude takes low second place to doing whatever is necessary for safety - of horse or handler. So the diff in successful use, IME has been when a horse isn't actually or significantly afraid of the situation - he's not pulling out of fear of being trapped.
And perhaps it was because I was thinking of 'punishment' in behavioural terms, not whacking the horse or whatever, but just anything that is an undesirable stimuli to a horse. Eg. in this case, putting significant pressure on the lead. Esp when, due to elasticity, that pressure will not cease the moment the horse stops pulling back - they have to not only stop pulling but come forward before they 'release' the pressure.
Just a case of terminology then. I consider it much less restrictive than hitting the end of a fixed object. Nor do I consider it a punishment, no more than learning to be tied could be a punishment. Its just a different type of lead rope...
If you consider training that teaches the horse to release from pressure a punishment, then nearly everything we do with a horse would be punishment.
Horses used to be tied to a pole in the ground, outside, with the tire inner tube attached. They were left to figure it out for themselves, and most never had a problem after that being tied. It was the first step of saddle training. I prefer standing right next to the horse and teaching him what to do, for the horse's safety.
The horse quickly learns to step forward, so has a lot of control over the situation. Anytime we turn the control over to the horse, the horse has the opportunity to make their own decisions, which is a confidence booster.
IMO "tying" the horse to one of those rings that allow the rope to just slip though is just teaching the horse how to break free. Not something I want to teach my horse!
Horses do not like pressure on their poll, and naturally will fight to resist it, but giving to the pressure is something that they need to learn how to do.
I've been riding/working with horses for almost 50 years now, and have seen a lot of training methods come and go. Some methods I am still using from back when I was first learning to drive and ride from a very experienced older man. Back then we loaded the horses in the back of a truck to take them to the fair. I and my friend rode back there, standing up, with them
As I frequently say, everyone has their own methods that work for them, and the OP will need to learn her way around all the advice to discover what works for her and her horse.
If I didn't think this method would help her, I wouldn't have mentioned it. But calling tying up a horse with a different type of lead a "punishment" may lead her to not try something that might help her.
Some old-timey methods are still relevant today...