IMO, you need to understand exactly what is being described as a 'push' ... and where in the swing you are speaking of.
IMO, someone initiating a swing with a 'push' is making a mistake. For me .... I want the force couple type feel of the hands turning the barrel at swing initiation ... and not a 'push'.
From the power-vee at 'launch' to the power-vee at the 'RVP Connection Point Position' are you really 'pushing' .... that isn't my feel.
Perhaps the confusion comes from the 'RVP Connection Point Position Point' onwards ..... clearly extension is in progress here .... the hands in a sense are working away from the body's rotation and then releasing the barrel.
Bat drag being the hands losing ground with the bodies rotation, or the hands losing ground with the bodies rotation, very bad.
But what Cabrera is doing with his hands appears to be Leading the bodies rotation.
And the swing that Williams is describing as the "push type swing" and from his images, sure looks like Cabrera's beautiful short swing.
another area of Push, might be from the word you use "Release" as I can swing using force (firm) with my wrists, through contact and beyond, or I can Pivot the barrel and then release, or I can just whip the barrel. I can release at any time in the swing.
Would using force also be push?