The argument for why hinge action is irrelevant, as I understand it,is that the ball is on the face of the club for such a short period of time that there is no effective difference between the direction of the club face at impact and that of the face at separation. Because nothing happens between impact and separation, there is nothing that hinge action does.
In discussions with those who advocate the irrelevance of hinge action, I have asked why then does hinge action seem to make a difference that can be seen and felt in, for example, the simplest of shots (as remarked by OBLeft). The answer I received was that hinge action sets the face prior to impact, which then leads to the ball flight. Horizontal hinging tends to a closed face at impact, etc. The point that is made is that nothing significant happens during the impact interval because the time the ball and the face of the club are in contact is so short.
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