You are putting words in my mouth. I am telling what I actually verified. Amplifiers with lower THD and IMD often sound worse than those with less impressive meausured parameters. Ergo, the measured parameters are not relevant. We need to find the actually important paramters and measure them.
But “sounds worse” in this case is relevant only to your preferences and to the preferences of some N of listeners, where N is totally unknown. The parameters you believe amp manufacturers should measure are therefore only relevant to your idea about them.
THD, SNR, frequency response and many other metrics are easy: they define either accuracy or precision. If you want more than that, add external affects hardware or DSP. The purpose of the amplifier is to amplify.
It is relevant to a very large number of people, and that is why it is reflected in the price of the equipment. A very well known engineer, who has not ever peddle snake oil, Nelson Pass, sells his rather primitive audio equipment at high prices. Jusdging
You seem to be highly inexperienced in the subject, THD, IMD etc are parameters that are measured on highly artificial signals - singke sine waves or mix of small numbers of sine waves. Real music signals more resemble white noise than clean sine waves, and there might be hundreds of different very subtle modes of distortion, that are very difficult to measure but which have very significant influence on the precepted quality of the sound.
It’s not clear to me how one person selling boutique equipment at high prices is indicative of any flaw in measurement methodology. There are many companies doing this, of dubious real value to consumers. How is Nelson Pass different, and how is that relevant to what we’re discussing?
