Assuming we're on the same page, we're talkin about a few inches of head movement here. (if we're still talking about a Centered motion..."base of neck" Center)
It really feels like nothing to me (err at least not like that)...
A few inches is the difference between the sweet spot and a shank or even whiff. The difference between compression of the ball and hitting behind the ball. Inches are significant in the golf swing.
That said I think Jim Hardy was onto something when he said those that swing their arms upright (i.e. Watson) would benefit from some weight shift and consequent lateral head movement in the backswing (to give the arms enough time to swing down in the downswing) and those that swing their arms flatter (i.e. Hogan) should keep their weight centered and the head should not move.
As an aside I believe a really upright arm swing plane is less than ideal, but certainly works great for some.
Matt
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"In my experience, if you stay with the essentials you WILL build a repeatable swing undoubtedly. If you can master the Imperatives you have a champion" (Vikram).
The reason you can't sustain the lag is because you are so eager to make the club move fast (a reaction to the intent of "hitting it far"). So on a full shot you throw it away too early, which doesn't happen for your short chip. (bts)