You realize that the entire purpose of a bit is to create an unpleasant sensation in a horses mouth encouraging them to yield to pressure.
True to an extent, but only to an extent. Yes, horses have to be taught pressure and release, and the initial introduction to and training in a bit will be different and unpleasant. But in the well-schooled horse, there is no longer a need to pull hard and squash the tongue and so on. A slight flick of the reins and jingle of the shank should accomplish all that is needed.
EVERY bit has the potential to damage the horses mouth.
I have personally seen in person real live horses not on the internet that have been ridden for many years in a TT without it destroying thier mouths and ruining thier very lives.
I don't doubt it. A TT is highly unlikely to break a horse's jaw, as some people claim. But the point is not so much that it is cruel as much as it is ineffective. Nothing about the bit mechanics are balanced right. The cues are inconsistent and very confusing to the horse. A well-trained, patient, saint of a horse will probably ride just fine in a TT, despite the crap going on in his mouth and the discomfort from the twisting mouthpiece. A horse who is initially broke to ride in a TT, however, will likely toss his head or gape his mouth.
If you don't like it then don't use it ( I don't) but it is not inhumane or cruel.
See above, and I won't use one.
Every broken mouthed curb has the same action as the TT.
That is not true. See the link I supplied earlier. There is a segment comparing Tom Thumbs to Argentine snaffles--they absolutely do not work in the same way or have the same effect.