A measurement of THD is a measurement of THD. A measurement of frequency response is a measurement of frequency response. To extend those measurements beyond that is not science, it is pseudo science.
I doubt I will make any impact in this discussion as a discussion of measurement takes a level of understanding of several topics that is likely beyond most people participating in this discussion.
Stereophile presents a limited set of measurements.
Audio Science Review presents a more comprehensive set of measurements but are limited in time.
Do engineers and manufacturers do more tests? Some do. Many do not. Many of the tests may not be for sound. For speakers, I expect many small brands don't have the equipment or knowledge for extensive testing, certainly not for speakers.
I wrote a long paragraph but deleted it. I would suggest reading this and coming back: https://www.ap.com/technical-library/using-multitones-in-audio-test/ I don't think this existed 20 years ago or even 15. "The characteristics of a multitone waveform (e.g., spectral content, histogram, crest factor, etc.) give it a much closer resemblance to typical audio program material like music or speech, than a single sine wave"
The speaker testing we do is much more comprehensive. Electronics are nice, predictable, and repeatable (maybe not that SET amp). Distortion normally scales with level, frequency response does not change with levels (it may with load). Nice. Easy. Speakers are nasty beasts. Distortion can be low then rise rapid, and is different at every frequency. Impedance can change with level, which can lead to changes in frequency response (and crossover). Different drivers have different dispersion. Distortion is not consistent across angle. Voice coils heat up leading to parameter changes and passive crossover shifts.
I would spend far less time worried about whether your electronics are tested adequately and spend a lot more time worrying about whether your speakers are tested properly.