The error is here "what about the thousands of feet of crap copper cables in your walls, huh?" - Its the last 6 feet of cable that supplies the power, believe it or not, out of the space around the cable, weird!
No electrons (i.e zero) from the power station go anywhere near your amplifier, all ac does is jiggle them an inch one way or another. How can they get from the power station if they are moving back and forth? The key electrons are in the last 6 feet of cable! Only in DC do they drift very, very slowly, but power is instantaneous => Poynting
The thing that moves is the induced E-M field caused by potential difference moving electrons one way then the other. This wave moves at approx the speed of light which is why a power switch seems instantaneous. Power per unit area is given by the Poynting vector going radially into the wire from outside the wire. In a mains cable, the power is kept within the dielectric coating into the wire, Poynting vector is zero outside the dielectric if its thick or good enough
S =
E x
H
Where S is the Poynting Vector, E is the electric field vector, H is the electric field vector and x is the vector product
en.wikipedia.org
https://commons.wikimedia.org/wiki/File:Poynting_vectors_of_DC_circuit.svg
It applies to AC and DC
What confuses engineers is the adherence to the Drude model of electricity from the 19th century
https://en.wikipedia.org/wiki/Drude_model
Like many models, it is useful for explanations and engineering calculations but don't mistake it for reality. Reality is Maxwells equations and quantum mechanics. Why use Drude, it's good enough most of the time and much easier to work with, after all why use General Relativity when you can use Newtonian mechanics most of the time. Models are useful until they are not
Its the difference between physics and engineering, this is under grad physics stuff(admittedly they don't explain it well, I never understood line integrals till years later even though I could calculate them)
If you want to calculate resistance, capacitance and inductance the hard way there are plenty youtube videos
So perhaps the cable salesmen are not completely wrong as
@tima alluded to but I find they dumb things down soo much the explanation may sound fishy (I don't work for any but my first degree was physics & astrophysics, we always had a friendly rivalry with our fellow engineering grads ;-)
Don't believe it then google it or buy/borrow a physics book on EM theory. Think about it, do you see circuit diagrams with length on them?