Extending is not exclusive to the pelvis and thorax in the follow through, the neck also side bends and extends as well. The neck extending and side bending on the follow through does a number of things. We will talk about the most two important pieces.
#1 – It helps keeps the axis of the shoulder turn stable on the through swing and keep the shoulders turning in a circle. From the down the line view this will help keep the golfers head on the wall.
#2 – The neck tilt allows the golfer hitting outward at the ball long enough, so the ball will push and draw. If the head flashes forward from the caddy view this will cause the path of the club to swing across the ball.
Take a look at the two pictures posted. The left picture has the least amount of side bend and extension in the neck and the pelvis. The right picture has the correct amount of side bending and extension in the neck. So remember not only does the pelvis and thorax extend on the follow though the neck does as well.
What you can see from the DTL (down the line) pictures is the head coming off the wall on the left picture. The inclination is not stable because the neck and hips have not extended or pushed forward enough. One would expect with the head coming off the wall that the balls will push or start farther to the right. Also if the golfer kept the neck flexed forward and kept turning the path of the swing would go slightly across and there would be some pulling.
The golfer on the right has a stable inclination to the ground because the head has stayed on the wall. The swing will resemble more of a circle and the shot pattern will be much tighter and more consistent.