Ok I work in the medical field and follow evidence based science so I know how it works. I get what you are saying. Let me ask you this out of interest… If you were building a crossover for your speakers that you considered your end game speakers, as I did, would you just use the cheapest of components available that offer the correct value? If you know that none of the commonly used speaker measurements would not find a difference.
Of course
@Jim Taylor can speak for himself (edit: and it looks like he did while I was typing this!), but from my perspective you ask a very reasonable and important, practical question.
Were I building a crossover for my end-game speakers - or for any speakers that I intended to use as my main listening speakers and not just for experimentation - I most certainly would not use the the cheapest possible components that offer the correct values.
The issue, though, is why I would make that decision, and on what basis I would choose the more expensive components:
1. I would be concerned about the cheapest components mainly because I would not feel secure that every individual sample I would buy would actually measure to spec, and I would be concerned that even the ones that did might not retain the correct values/operating integrity over time, in-circuit, with the stresses of use, heat, wear and tear, different power/current conditions, and so on.
2. I would choose better components based on the best information I could glean about likely reliability - in other words the likelihood that they would be to spec when received, and stay in spec for as long as possible when installed and put into regular use over a period of years.
The crucial points that follow from this are, as I see them:
1. For point #1, individual components can be measured, both in and out of circuit, both upon receipt and over time. Of course, I would not want to have to go through the hassle of taking apart my speakers every few months to see of the crossover (and its components) was still performing to spec. And even moreso, I would not want to have to worry - or even give it a second thought - that when I was listening to music, it was coming through a crossover network that was inferior to the one I'd designed and built. The crucial thing here is that such problems would be measurable, and therefore as Jim says they would be "external" to my own personal perception or impression. But as a practical matter it would be highly inconvenient, and undermine my daily listening enjoyment, to have to take those measurements once the speaker was built and in use.
2. For point #2, the issue is similar: it's not about sonics that somehow elude our ability to measure them. Rather, it's about the fact that as an individual I have limited knowledge (some of us here have less limited knowledge than others when it comes to real-world knowledge of the long-term operational qualities of different electrical components). So I would do my best to pick quality components with likely long-term stability and reliability. But again, the issue is not that I know those components will sound better than the cheaper ones - the issue is the converse: I can only hypothesize, or make a somewhat confident prediction, about how components will perform into the future, and so I will spend a bit more to get ones with a higher probability of being trouble-free over time.
3. Finally, if these are my end-game speakers, and if I am building them myself, then I clearly have a lot invested in them: a good deal of money, a tremendous amount of time, and a lot of emotion - emotion because I'm putting in so much labor, because I aim to feel pride at having done it myself, because listening and looking at them once they are done will give me an extra level of pleasure knowing I built them, and a certain level of "high-stakes" anxiety because these are my end-game. This is supposed to be "it" and so I would likely want to make 100% sure I got them right. For these reasons I might very well buy some more expensive components, even if on a rational level I felt confident that there were some less-expensive components that measured the same and would be just as reliable over time.
But again, the crucial thing there is that I would do this as an emotional insurance policy, not because I felt confident that the more expensive stuff would actually produce better sound than the "good quality but one notch down" stuff. I would never think I could claim that the more expensive stuff sounded better - or rather, I could easily claim that it sounded better to me, but I would not claim that my individual experience meant there must be an objective improvement that is somehow impervious to all measurement.
So that's my $.02 on your question, for what it's worth.