I'd be curious to see the context of the quote
@geepers posted, but I don't believe Franko is saying that there is an unbalanced moment about the
skier's COM when carving and I think that perhaps there's a misunderstanding here. Purely from the frame of reference of the ski, as a shaped ski tips over further and further more space is created between the snow (let's assume super firm icy hard pack for simplicity's sake i.e very flat and little surface deformation) meanwhile the ends of the ski are still in contact and accepting the lateral grip frictional force perpendicular to the edge. An unbalanced moment arm (i.e torque) is therefore created at both the tip and tail of the ski since there is now less lateral grip force acting at the center of the ski from the edge lifting, thus the ski bends and arcs. This is what a skier is perceiving. Once peak edge angle is achieved though the ski does not bend further as the load is now evenly distributed and unbalanced moments resolve. The lateral grip force is the centripetal force that deflects you across the hill and you want to stay aligned with that force in the center of your ski.
Now imagine the opposite, if you had 150cm long 1/4 inch wall square steel tubing attached to your bindings (a "ski" that can't be bent both due to the straight shape and relative stiffness). As you transition your COM across your "skis" into the new turn there would be no unbalanced moment arms as the lateral grip force would remain constant along the length, they would simply continue straight across the hill as you the skier fall downhill of them, ouch. What the position of the skier COM really influences is the profile of the distributed load of that frictional grip force along the length of the ski by increasing it in the place where the skier COM is aligned with. In non-carved turns this causes differential bending along the length depending on where that distributed load resolves to relative to the center of the ski as well as allowing the portion of the edge furthest from where the COM is aligned with to slide. As mentioned previously, for carved turns you want the whole edge working simultaneously bending at the center, thus you need to be centered.
The problem comes given the fact that humans are not a rigid mass on a pole welded to the center of the ski. It requires muscular effort to control your joints to maintain the centered position since your feet/skis are moving faster than your COM is around the arc created by the side cut, the center point of said rotation is not the skier COM though, but the geometric center of the ski's radius. Rotation about the skier COM would necessarily mean tails not following tips as human legs are usually shorter than than 13-22 meter side cut radius of skis
. IMO rotation about the skier COM (looking top down at least) is pretty undesirable, e.g. losing your tails at the end of a carve and flying head first down hill.
My far from expert understanding of what Tom or Paul are talking about with their ever so slight shift from ball to heel through the turn when carving is that it's a real world implementation of this theoretical physics classroom model of carving. A slight bias towards the tips initially gets the tips engaged as you're coming out of transition and gives your brain time to manage the velocity differential of your feet and COM which inspires confidence. The aggressive pull through with the hip flexors at the end is because they're making incredibly athletic turns/transitions where they actually need to accelerate the feet even further to manage the large velocity differential between their COM and the skis' path.