The placebo effect argument works both ways. If you're of the mind that power cables won't make a difference, you'll not hear a difference. That, and you'll point to lots of other people who fell the same way and "documented" it.
In theory, sure. That's why I produced a double blind (or close to it anyway) ABX test to demonstrate my point. Do you understand how a double blind test eliminates the placebo effect? If not, there are resources online where you can learn all about basic testing methodologies. It's a staple in the Rx industry. Some people have called into question the utility of ABX testing in audio, but that's an entirely different argument that you haven't even started to address.
The only "documentation" I pointed out was a scientifically conducted test (no test is absolutely perfect) that demonstrated people, even audiophiles, could not hear the difference between power cords with enough frequency to demonstrate they were doing anything other than guessing randomly.
Tell me this: If the power mains cable manufacturers are so convinced, whey don't they use their considerable resources to demonstrate once and for all, via controlled double-blind ABX testing that their cables sound "better"? LOL
The burden of proof is on them - as they're selling a product they claim has certain benefits - and not on me, who is simply giving my informed opinion to the OP of this thread who asked some questions about expensive power mains cables.