The standard power cable provided by the maunfacturer is not capable of responding to the immense demands of tranient signals. More advanced designs allow the conveyance of enough power in a timely manner such that an amp can perform up to its full potential and reproduce those transients more faithfully.
I loathe to ask, but (a) what part --specifically-- inherent to the "advanced" power cable enables it to allow more power from the station / to the pole / over the lines / into your home through the walls after going through its own short run of wire? And (b) what part of the PSU system within the component senses and allows more current than what it is specified to engage .. a timely conveyance of it, as you say, to increase audio transients? Finally (c) what makes this wire magic so expensive that it is not within the cost/benefit analysis parameters of the manufacturers to include it with their mid to higher priced products if the difference is so easily heard? Thank you.