Objective vs. Placebo relating to system changes

I am continually baffled by the number of people that are convinced that changes to power cords, speaker wires, interconnects, etc. in their systems result is objectively real changes. While I won't go so far as saying that making these changes absolutely doesn't make a difference, I would love to have the resources to challenge people prove it to me and test it with my own ears.

Here's what I would do if time and financial resources were no object (I'm visualizing retired millionaires that are audiophiles).

I would build a listening room where the only components in the listening space were the speakers and the speaker cables coming through opening in the wall where the rest of the system was setup. The idea would be to allow the test subject the opportunity to create their system of choice and then have the opportunity to become very familiar with the system by spending hours listening. Then I would let them know when I was going to start changing different components on them on a very random basis and they should report any changes that they heard so we could link the changes to any potential changes on the other side of the wall.

Here's a short list of things that I'd try:

(1) I would replace the upgraded power cord with the stock unit.
(2) I would install or remove isolation (e.g. Nordost sort kones) devices from a component.
(3) I would replace interconnects with basic quailty products.
(4) I would replace well "broken-in" cables with otherwise identical new ones.

Depending on the results of doing these test slowly over a period of time I would consider swapping out some of the more major components to see how obvious a macro change was if the listener wasn't aware that a change had been made.

I can tell the difference between new and broken in speakers (on ones that I'm familiar with) so I know this break-in is very real and would also not be at all surprised with differences from amplifiers and analog sources being obvious. I'm not as sure about digital sources.

So the question is, what components in your system would you be confident enough to bet, say $1,000, that you could identify that something changes if it was swapped out?

In my system I am sure that I could identify a change in amplification or speakers, but highly doubt that I could do the same with any cables, isolation devices, or digital sources. Maybe I just reduced myself to being a non-audiophile with low-fi gear?