The head is a freewheeling object at impact, operating on it’s own mass and dimensional characteristics. The heads MOI is just that, the heads MOI. In theory, the more stable the head, the less affect it will have on the shafts rotation, but the shafts characteristics will have no bearing on the heads MOI. Obviously if you have a shaft with a really high torsional stiffness (like 14 degrees) the resistance on the heads natural rotation up to impact will be less and visa versa on a really low torsional stiffness. However, at impact, it is the heads MOI and it alone that determines how much rotational movement there will be of the heads mass. The head rotates around it’s own center of gravity at impact. That being said, it is reasonable to assume that a really low torque shaft vs a really high torque shaft would make the head rotate less on off center hits if we were to measure the rotation around the shafts axis. Very difficult to measure because there are so many other dynamic shaft movements that take place at the same time. Also, the variation in torsional stiffness between shafts is not that great (generally 2 to 6 degrees in raw shaft torques and less once installed). The trade off, if you want to believe that a lower torsional stiffness improves the rotational dynamics of the head around it’s cg (which it doesn’t), is that a lower torsionally stiff shaft will feel stiffer or more harsh than one with a reasonable amount of torque.
Good question and one that is not easily explained, as you can tell. The head rotating around it’s own mass and dimensional characteristics, being a free wheeling object a impact, is something that is difficult for some to get their head around (me included). But, it is a fact. I think it’s easier to come to grips with it when you realize that once the shaft unloads (which it does before impact), the head is driving the bus, not the shaft.