There are two big reasons to use SINAD: It is so super simple and it is easy to compute!
But otherwise I am not convinced to use SINAD as a ranking number for SQ. [I use it as some kind of safety number to be below the threshold of audibility.]
For ranking the performance I would like to include linear (FR) deviations, harmonic (and other non-linear) distortion and noise.
And these aspects would have to be weighted according to audibility.
Linear deviation (FR) becomes audible around 0.1dB or 1% of amplitude. But this depends on the frequency range and maybe weighting with ERB-scale can account for this. [And there is of course the width of the deviation.]
Harmonic distortion becomes audible around 0,1% (-60dB), but this depends on frequency and number (frequency) of the harmonic products. So we would need some kind of two-parameter weighting at least. Level dependency might have to be taken into account, too. I do not know of any robust science on that.
[Just weighing the harmonic products by Fletcher-Munson might be a first guess, but there is masking, which is more complicated.]
Other non-linear distortion (IMD) is important too, but it seems to be rather closely correlated to HD for almost all electronics (and speakers?)
Noise will become audible around 0,01% (-80dB), but again this depends on noise spectrum. Fletcher-Munson (A-weighting) seems to be the obvious choice.
All this are only ballpark numbers and depend on program and use case.
This kind of weighted sum would be a better choice in my point of view.
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But now it is not so simple anymore, and there is no consensus, of course.
And the question is, how important is it anyways? In electronics it is not a big problem to stay below audibility (unless using tubes) and in speakers SINAD is not the number used at all.