Some specs matter and some don't.
An example of a spec that matters is noise. Another is bandwidth (which ideally is 2Hz to 200KHz to reproduce 20Hz to 20KHz properly...)
An example of a spec that hardly matters is THD. The reason this spec has small importance has to do with the way the human ear/brain system interprets harmonic distortion, which is to say it interprets it as tonality. In this regard, the 2nd harmonic is musical and not easily heard by the ear and for that reason quite a lot of it can be present before it becomes objectionable. OTOH, the odd orders (5th, 7th and 9th) are highly objectionable and for that reason trace amounts that are hard to measure can be quite audible (the ear/brain system also uses higher ordered harmonics to interpret sound pressure, so it is very sensitive to these harmonics).
So- when a low THD is seen in the specs, its likely that it will not containing much in the way of the 2nd order and is instead likely to be almost entirely higher orders, on account of the fact that global negative feedback has likely been used to obtain the THD value. Loop feedback, while effective at reducing distortion, is not effective at eliminating it altogether- its use will surely mean that elevated higher orders of harmonic distortion will surely be present.
This is why you will see a debate in high end audio about the use of feedback. Because the ear uses higher harmonic orders as loudness cues, it is essentially more sensitive to their presence than excellent test equipment. Audiophiles have words for such low distortions: bright, harsh, brittle, chalky, etc.
These descriptions will often accompany equipment with low THD values. We have seen these comments around as long as the internet has existed- my point here is certainly not debatable!
Now if the specs showed how the harmonic distortion existed in the amplifier or preamp (showing the lower orders and the odd orders as a separate value), especially in terms of a signal that was in constant change rather than a sine wave, the result would be a distortion spec that told you exactly how that amp or preamp would sound. We are a long ways from that- right now the harmonic distortion spec can be considered vestigial at best.
There are other specs, like damping factor, the are often given a lot more weight than their due- in the case of damping factor, there are no known speakers that need more than 20:1, so why is it important to have a damping factor of 100 or 1000?? But we see this touted all the time... really, a lot of it is marketing and not actual science.
