That is a tough question to answer, and there aren't too many, or any articles that authoritatively addressed the related topics. It may be because it is mostly related to a hobby type of thing, if it was medically related, life and death kind of deal, the mystery would have been solved by scientists and engineers.
I don't remember seeing any, but it might have, in the reviews of active speakers. For passive one, SINAD should be irrelevant because of the noise part, so you will typically see THD measurements, not SINAD that is THD+N combined.
All else being equal (unfortunately all else usually are not equal) basis, I would want the lowest possible THD+N because then I don't have to worry about things like: does the devices have low THD, but the harmonics are of high order?, would that 0.08% THD+N audible?, how about the % during those 20 dB peaks in music, how about the % being higher in high frequencies, affecting the sound quality of my favorite instruments (
Instrument-Sound-EQ-Chart.pdf (guitarbuilding.org) etc.
Is 70 dB good enough, to me it is, as long as it is+ for the worst case scenario.
It may be possible that, in pursuance of the lowest possible THD+N, and extended FR into the ultrasonic range, an amplifier manufacturer might have introduced another issue that could be more relevant to perceived sound quality for real world applications. That is hard to know, that's why I like to qualify my points with the "all else being equal" catch all phase. You are right, we want what we want, and I would add that sometimes we don't know what we want, even when we think we do.