IF one was to suppose that all of the wiring from the power plant, to the house, to the wall socket, was all 12 ga Romex or equivalent; and IF the standard-issue IEC cord that one person has is 18 ga, and say 12' long, then I could start to see some potential for say a 6' long 12 ga power cord to perform measurably better than the stock cord. IF it turned out that this was the case, even then the benefit would be exclusively "a bit more power", and nothing whatsoever to do with noise filtering, time-aligning, wave-smoothing, or any of those other garbage claims.
So then the question becomes: are there some amps out there that may be slightly louder or slightly better able to reproduce big low transients if they are fed some small percentage more power (able to draw a bit more current, for example) before the rectifier stage?
That's a question I'd truly love to hear thoughts on from Bob, Mark R, et al.
Of course, this whole premise comes crashing down if there is skinny wire leading up to the wall socket, or if the stock IEC cord is short or of sufficient gauge.