All the parameters in your equations are valid. Except Snake Oil. Might want to add the dampening of the conductors inside the cable. When current flows through a cable it flexes. A big air conditioning unit startup pulling 200 amps inrush. An untethered cable will flex or move. Extreme, high tension power lines shorting will actually whip around like a snake. Obviously, there is less movement in what we speak but does alter the reactance of the cable and have an effect.
Also. I think it has something to do with the power supply in the connected unit. Not so much feeding power into the unit, but how the cable reacts to the counter emf that the unit is trying to push back into the power cord. Creating standing waves on the wires in the cable. The wires in the cable flexes on those standing waves. And find a happy spot. Break In. Ultimately settling the Phase Aligning the dc voltages out of the power supply. After all, It's all about the DC Phase Alignment
I think we both have too much extra time on our hands and need to get a hobby.