The mistake both you and Itpro are making is the assumption of "unused axle" and "axle overhang". Your knowledge needs updating with the specifics of modern karts.
In a modern kart, the hubs overhang the rear axle. By changing the rear width you are also changing the amount of axle within the hub. By cutting the axle you get the same change (amount of axle in hub), without the change in rear width.
I'm sure you would accept that the interface between hub and axle would be particularly weak (flexible for want of a better word) if there were just 5mm of axle within the hub. I'm sure you would also agree that this interface would be particularly stiffer if there were 100mm of axle within the hub. As such, you can only agree that altering the amount of axle within the hub will alter the stiffness of the axle/hub assembly.
Finally, the stiff/soft axles as supplied do make a difference to handling. They may use incorrect nomenclature or scientific justifications but that doesn't alter the fact that they change the handling of the kart.
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