I’m also worried about how much of the harmonics in the music is LOST by the amp?

Reference speakers are on average starting at $15-$20 k for a decent true reference speaker on Average considering today $50k is  the mid high end range  for a speaker, there are a few exceptions to the Rule.
one key is a solid cabinet , High quality drivers , and premium Xover
components. Many companies use $30 tweeters and that’s ok for a under $5 k 
speaker ,name brand such as Accuton, Scanspeak ,Seas ,in their upper range are premium and more $$ costly but, much lower in THD . Speakers sold direct 
like Spatial Audio labs ,made in U.S.A  open baffle speaker but in the X series 
all drivers are premium especially the custom Beyma AMT tweeter- upper midband  and under $10 k a steal beating  many speakers  2x+ Their cost.

If we can’t measure the musical information lost throughout the chain, the measurements we do have about what gets added in terms of distortion are a smokescreen.  If you lose 25%, but add negligible distortion, you pretty much still suck.  Right?

I mean, signal to noise ratio would seem to be the most relevant stat in common usage, right?

I mean, signal to noise ratio would seem to be the most relevant stat in common usage, right?

Even when it's below audible levels, I have always wondered if it can contaminate the sound.

A very strong SNR of 120dB is almost certainly beyond audible range, but could be important for the fragile harmonics.  I’m sure there are people here who know this scientifically.