4 Head and chin have stayed stationary as body moves front shoulder around and brings rear shoulder forward. Shoulder rotation is just as important as hip rotation. Now, suppose I pop my hips and rotate the shoulders but keep slack in my arms so the hands don't move. No matter what batting technique we choose, the only impact on bat-speed is when force is transmitted through the hands to the bat. Lateral and rotational movement do not happen at the same time.
Some batters move laterally in preparation for the swing.
Barry Bonds and Ken Griffey Jr. have little or no forward movement even in their timing step - they pick up the toe and set it back in the same spot. As the batter prepares for the swing, the lead knee, hip and shoulder should rotate slightly away from the pitcher. This should bring the hands, center of axis, and pitcher's mound in line. This is not a 'coiled' position. We don't want to stretch muscles around locked joints.