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In 2-H Mr. Kelley wrote, ‘Though the “Head” Pivot Center is recommended, it is not at all mandatory. The important thing is that the true Swing Center for ALL COMPONENTS is around a Hinge Pin with one end at the top of the Stationary Head and the other in the ground, precisely between the feet, with no regard for Body Location or Position at any time.’
You can move your head if you choose to but what advantage is it?
Why not keep it stationary?
It is too bad that Gulbis, Creamer, Woods, Baddeley and others do not set their head at impact fix.

Yes and why did Homer choose the stationary head? Because he used his eyes focused on the ball as the easiest way for the golfer to determine if the head was stationary or not.