Yes, transmission lines have known losses which need to be accounted
for and factored into their designs, but that has nothing to do with
the current discussion. There are no long distance transmission lines
in a residential or even commercial property, so the losses from such
lines are irrelevant to the current discussion. I suspect the reason
you were never taught that is because this is far outside your area of
expertise, which I believe is what you said in a previous post.
Take your example of the electric dryer. If you have two dryers, one
designed for 120v and the other designed for 240v, the 120v model will
draw twice as many amps as the 240v model. Both dryers will use the
same number of Watts, (because P=IE), assuming the only differences
between the two models are the voltages they are designed to operate
with.
If we're having a technical discussion, then P (power) is expressed in
Watts, not amps. Current draw refers to amps, but power refers to
Watts. Watts are the product of amps times voltage. (P=IE)
If you're saying that "P equals IE" is wrong, and should be restated
as "P is approximately equal to IE", well we better get the textbooks
updated with this new formula. In the meantime, yes, if E is doubled
then I will be halved and P will remain unchanged. It doesn't just
work that way in the textbooks, it works that way in the field, too.
Not a bad idea to dust off the books now and then.