I think you're right to question where in the chain to try to fix or compensate for problems in music reproduction. It would seem to make sense to fix things as far upstream as possible, but that isn't always easy to do.
With regard to Nelson Pass, I watched a YouTube video of an interview he did with Steve Guttenberg that mentioned the distortion profile issues briefly. Nelson was careful to state that he didn't actually add second or third harmonic distortion to some of his amps. Instead, he simply chose not to suppress those lower order distortions as much as he could have in the circuit design.
For my own listening, I don't look at ultra-low distortion specs in an amp as a sign of sonic purity if those specs are associated with any harshness or brightness in the sound quality I hear at the downstream end of the chain. But adding in a lot of extra distortion doesn't seem like an ideal design strategy either.