NO, cost per kwh does not change....the caveat in your statement is "adequate wiring".
Real world wires have resistance and you will lose a small but measurable amount. The voltage drop as a percentage of the total becomes smaller and smaller as the voltage goes up.
Let's look at 100 feet of 10 AWG wire carrying 5 amps. At 110 volts I lose 1 volt at the end for .91% voltage loss. At 440 I still lose 1 volt but my percent loss drops to .23%. This is with a 10 AWG copper wire at .0009989 Ohm/foot.
It just depends on what you mean by adequate wiring. To cut the loss in half in this example you could go to 7 AWG wire. At some point it gets ridiculous.
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