First, the OP reports Amir as claiming confirmation bias in "analytical mode": "when he switched to an expensive cable he heard improvements, but when he switched back to the cheap one, he also heard improvements because the brain switches from 'music enjoyment mode' to 'analytical mode'.” If this were true, however, one could in theory continue switching out "better" for "lesser" components, experiencing an "analytical mode" confirmation bias each time, until one was left with a Walmart rig (that is, a system we would all agree sounds terrible; I'm not impugning Walmart, merely coining a shorthand). If every change I make to my system results in a subjective impression of improvement, I could never move forward at all. This is tantamount to just saying: there is no audible difference between systems. But that is obviously false. So this methodological claim is logically flawed.
Second, as one other contributor to this thread has written, the brain's memory for subtle auditory cues is extremely short. Therefore, the only way to judge whether or not a given system change causes an audible difference is by instantaneous A/B, or better still, A/B/X blind testing. Again, this well established neurological fact is inconsistent with Amir's reported claim.
Third, as has also been mentioned here already, loudness needs to be very carefully matched between A and B, which is often extremely tricky to do. Louder will almost always sound "better," even when the difference in db is so slight that it isn't perceived as a difference in volume level. This is why people claim balanced cables sound better. XLR cables are advantageous in certain circumstances, but not in any that are relevant to home audio systems; in fact, for home audio, balanced is slightly (measurably but not audibly) worse. However, balanced cables are a few db louder, and so often are perceived as sounding "better."
Fourth, we're talking such subtle differences here anyway that a host of what might be called psychoacoustic phenomena become much more relevant. It's a little like wine tasting. The chemistry of one's mouth, which varies with the food you've eaten recently, with the state of your digestion, and a lot of other things, as well as one's mood, the company one is with, and so on, will affect one's impression of a given wine, which makes it very difficult to say that a given bottle is better or worse than the very same wine tasted on a different day.
Finally, the wine analogy perhaps shows why, despite the fact that the brain has too short a memory of subtle sonic differences to make comparisons over extended listening times (hours or days or weeks), it is still that long-term experience one must try to evaluate. Although the same bottle of Napa Cab from 2016 will taste differently on different days, or at different times of the same day, it is still possible to know with confidence that I prefer the bottle of Screaming Eagle (or whatever) to the Walmart Special—or even to a wine comparable in price and reputation to the Screaming Eagle. Similarly, I know with some confidence that I prefer system X over system Y as a result of hearing both repeatedly over a long period of time. It can't be that my brain is comparing subtle differences only evident in instantaneous A/B testing, and yet it is just as surely the case that I can, and do, have psychoacoustic preferences that are consistent over long periods of time.
