The crux of the reasoning can be found in chapter two. The line of compression.
As mentioned, 'the' plane is not the clubshaft, but the line of force between the hands and sweetspot.
that is a very critical part of TGM to understand.
For the physics of chapter 2 to create maximum compression, plane shifts should be kept to a minimum, because any shift is likely to decrease the force and efficiency of the line of compression (that said, there are more advanced discussions to be had around shifts and power generation, suffice to say from release point through both arms straight, any shift is not efficient).
As far as the body's role, keep in mind that it is the hands that must retain the relationship with the plane line, the body must just comply (see Ted's clip of his wacky pivot 'hit' in the gallery)
In a nutshell, the body must move in a way as to
a) allow the hands to retain the relationship to the plane line and
b) get the right shoulder moving down plane with as much of the body's mass as possible supporting impact while maintaining a stable center
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"Support the On Plane Swinging Force in Balance"
"we have no friends, we have no enemies, we have only teachers"
Simplicity buffs, see 5-0, 1-L, 2-0 A and B 10-2-B, 4-D, 6B-1D, 6-B-3-0-1, 6-C-1, 6-E-2