You agree there is some point in most games where, if you played that game a 1000 times, player B would win only 50-100 of them. You just think once you reach this point, there are only a few (how many, 20?) moves left of the game. I think you are incorrect in this assesment.
I haven't seen the previous discussion on invisible. Maybe there are some other ideas to save the ability, since you were right about my initial idea not working. Anyway, my opinion is that if there is not a good fix, it should be removed. The huge boringness factor of the games dragging out because of invisible, is much more important than the fun factor of having that power. You might disagree with this, if you have another idea about what is entertaining than I do, but I don't see how you can say that I'm "wrong" about it.