It's like saying the truck which drove the water to the soup factory makes a difference in the taste of the soup. Well, not really, but you see what i mean?
Adam,
Logically speaking, I agree with all your examples of why a power cord couldn't possibly make a difference in the sound. I sat and thought out logically why it shouldn't make a damn bit of difference. But I rarely say never, so I am always very open minded on topics that are well beyond my general understanding. Even on topics I know and understand well, I leave room there too. It's healthy.
I tried a few times and thought I might have heard a difference, but when blind tested, I was inconsistent. So I was very much convinced that it wasn't an area worth pursuing much.
I tried it again a few weeks ago while I had someone over listening to speakers. We definitely heard a difference. Me and the other fellow agreed we would simply switch back and forth between PC's, listen, not look at each other to tip each other off, then at the end of the session discuss it, and compare experiences. We heard the same differences. I don't recall if the other fellow was a believer in cable differences or not. He has a background in electronics.
After he left, another friend stopped by, and we were hanging out listening to music and I decided to do the swaps again. He didn't know what I was swapping out. I told him I was going to try something, didn't tell him what. I just asked him to tell me if he heard a difference. So I went back and forth a few times. He's got real good ears. Better than mine. He heard a difference as well. He has an EE background, and a background in telecommunications from his days in the Army. He is a total skeptic when it comes to power cords. He has zip cord speaker wires in his way mega buck system. He heard a difference.
Both gents are AudioCircle members. We all heard the difference.
Funny thing was, we all liked the stock cheapo power cord vs the expensive one.
I'm not trying to suggest that cheap power cords are better, just that we heard a difference, and agreed that one cord sounded better in my system than the other. I've spoken to a few experts on the topic, and have been told it's not hard to make a PC sound different from another one.
Honestly, I wish I never heard a difference. I've got enough things in my life to agonize over.

If someone wanted to question my sanity over what I thought I heard, my response would simply be, "bite me". As sure as I'm typing this, I heard a difference in the 2 power cords we tested. Do I think I could do the test that we did with those particular cords and be consistent. Yes.
What does this mean for me personally? Not much really. I'd rather spend my money, time on room acoustics, and better components than cords, but, to each his own.
Cheers