The problem with a "hoof chain" is that it's a classic "anti-training device."
With a "training device" you use it, get a result, and then quit using it. If you use, say, a crop or a spur to induce an action in a horse when you get that action you stop using the device. The end of the device's "pressure" or "contact" is the reward for proper performance. Any good horseman knows this. It's an "on-off" system.
Some training devices/aids, like reins, can have a continuum of use where pressure can be regulated from on, to some, to off.
The hoof chain, on the other hand, is always "on." It's action is always constant. If the horse performs incorrectly the device exerts pressure. If the horse performs correctly the device exerts pressure. It only ends with the physical removal of the device. This is counter to about every theory of horse training I've ever read. This leads me to the belief that their use is the sign of incompetent or time/money driven training (a shortcut). Not all shortcuts are necessarily bad, but this one is.
Also, the residual effect of the chain is very short lived. Remove the chain and within a few minutes the effect is lost. If it were otherwise you'd only see chains on young horses in training, not aged horses in work.
A "kicking chain" is a very different thing. It only "bites" when the horse kicks. The horse soon learns that kicking is very painful and, at least while the chain is worn, the behavior goes away. I'm told by some that the effect is, in fact, fairly long lived. Some have said re-application can be required from time to time, but this is not a universal thought.
I hold the same view, by the way, on the other common "action devices" (long toes, heavy shoes, pads, stacks, excessively pared soles, etc.).