What does listening to a speaker really tell us?

Absolutely, Rockvirgo!
For this reason, in a practical sense, I'd rate a remote volume control more important than a "technically superior" one in most circumstances.
There seems always to be the "right volume", although the best systems seem somehow to work in a wider range of "close enough".

Fabulous topic with existentialist leanings, I love it!
For mine, we walk a tightrope in "Audiophilia". There is this side that says "accuracy" is what we need, that what comes out of our speakers is as close a reproduction of what is going on upstream. What IS this accuracy thing anyhow?
If I want a "kind of accuracy" I can get vanishing-low thd from a seventies integrated SS amp with bucketloads of feedback. But does it "make music"? Not for me.
As for the "musical" thing, what is that? What makes a musical "connection" to me is another person's poison.
Recreate a "live sound"? This is always our reference point, it must be. Someone alluded earlier to the notion that live music "kicks your butt" or to that effect. Doesn't it though? There is nothing "polite" about a trumpet played with passion. So for me the "smooth, laid-back sound" doesn't cut it, it doesn't kick my butt. For others, that kind of sound just might "welcome them in to the performance". So be it.
So for me, I want a speaker that makes it all "HERE!", as much as I can.
Never having been blessed with a system that simply Does It All, I make my compromises how I think they work best for my way of appreciating the performance. In a way, since we can't get a "perfect" speaker/system that it voices, you kinda choose your coloration, and the more we do this audiophile thing, the better an idea we have of what that is, referring always back to live music.

Woking "across" some of the interesting perspectives above, I would offer this:
Last night when listening to a variety of music, it didn't matter how this might compare to a "live music event". It was its own thing. I delighted in the clarity of the female vocal, for its inflection and the message that was communicated. This observation on reflection; the magic of the moment was on a different plane.
In the final analysis, whilst the real thing has always to be our reference (and stands apart in truth), the thing we have has its own, not inconsiderable joys.
Which is why we do this.