"Two people can use a tape measure and both agree that a door is 72" high."
The fact that two people use a measuring tape with a scale to measure a door that they have to recognize by contrast is a highly complex, socially and culturally evolved habit. We are unaware of all the prior knowledge and the common differentiation, contrasting, description and scaling. And even measuring would not work globally. Because of different scalings, languages;-)
Why don't you start small? Do your homework! And the first step would be: is a change, a differentiation audible - or not.
The quality and complex recording and description would come in a further step. A sufficiently precise language exists in audio discourse. And: we perceive by contrast and describe by contrast: to make a statement more precise, we start to name what we don't mean;-)
... which is why those who are off the mark should always be praised, because they are the ones who contrast perception and description and thus make them more precise;-)
"But when do two people ever describe their personal experience identically?"
Language is always only sufficiently precise, identical. If the involved agree on sufficient accuracy...-)
They (personal experiences) are not objectively measurable, so there is no reference standard like the inch, in the case of the door height measurement.
In that case you are getting the person's description of the experience; you are not directly measuring it, minus any distortions of the person's interpretation and wording of it.
It certainly can be that, at least if its a discrimination test. If its only a preference test then descriptive analysis would likely not be used.
For descriptive analysis its typically necessary to make sure people have a shared perceptual technical vocabulary so they can communicate accurately as possible.
The "ideal amplifier" as always being the best choice for any loudspeaker listening testing is a common idea.
In my experience loudspeakers even the very best are deeply flawed devices that have strong interaction between the amplification used and the source material played.
Loudspeakers designers have to make design choices during the design process.
One of those design choices is what amplification to use when listening to proto types of their speaker designs.
Some designers use "only the best amplification" what ever that is, to voice their speakers.
The result is a loudspeaker that will sound as the designer intended with audio equipment almost no one has or uses.
Other loudspeaker designers (myself anyway) used equipment that was representative of what most of my customers are likely to purchase in the price range of the speaker being designed. The speaker will thus sound as I intend with most end users actual equipment.
When source material transitioned from the LP to CD my speaker voicing was adjusted to account for the quite different sound characteristics of source material present on CDs. The transition from LP to CD also caused re-evaluation in what was seen to be a "good" choice for the high frequency unit for a loudspeaker. Many dome tweeters at time time sounded just fine from LP sources but were unpleasant and tiring from CD sources.
So yes I agree that the interplay between loudspeaker, amplifier and source materiel is a very important point that can be devilishly complex and subtle.
I have not even touched the listening room interaction to any one loudspeaker as that is another elephant in the room so to speak..