You raise some interesting points, chiefly that the usual measurements of THD, IM and perhaps a few more esoteric forms such as TIM may not completely explain the story, insofar as it relies on the assumption that systems are mostly linear, and the most significant errors can be captured in frequency and phase deviations occurring in amplification and transduction, the latter being moving energy from electrical to mechanical forms in speakers and phonograph cartridges (IMO transduction could also embrace conversion not just in energy but also in forms of information, that is from digital to analog waveforms).
The non-linear errors that introduce new waveforms are assumed to consist entirely of IM and THD, which can be easily measured. That they may not tell the entire story is the consistent observation that we are not annoyed by levels as high as several percent in the case of THD, and even higher when the music is loud. But there are some irritating exceptions as postulated by Geddes in this
paper and tested in this
one. A forum discussion can be found
here and more papers on his website
at this link.
I'm not at all qualified to comment on the accuracy of these claims, but they are interesting and curiously largely ignored. Whether that is because subsequent research has shown them to be of trivial magnitude and therefore inconsequential, or whether they are an inconvenient truth I can't say. I just mention this in passing as your comments stimulated my recollection of the debate, but it may be worth pursuing in your quest to identify the "missing" measurements. So have a look at Geddes papers, in particular Part 2 which discusses the GedLee (the two authors, Geddes and Lee combined) metric.
