This comment covers much of what is wrong with common interpretations of acoustics.
> the human ear is largely insensitive to moderate variations in volume/frequency... but it's incredibly sensitive to phase.
No, it's not. The human auditory system is sensitive to time variation. Phase shift may contribute a time shift but only at frequencies low enough that their wavelength has reasonably relation to the spacing of the ears. For example at 10Khz the wavelength is far too short for 'phase' to impact arrival time. Ultimately what actually matters in this regard with the human auditory response is group delay, not phase.
> Phase is how we discern directionality (stereo), among other things.
As mentioned above, what matters in the context of what your saying is group delay, but that is far from the only thing that matters for directionality. The human psycoscoutic system is very complex, part of directionality is group delay, part of it is frequency attenuation caused by sound wrapping around the ear from the ear, part of it is a half dozen other things. 'Phase' doesn't come even close to being a catch all cause.
> To my ears, the best and most musical sounding speakers
And thus we've devolved from science, as this usually goes. What on earth does 'musical sounding speakers' even mean?
> It's very easy to measure frequency response. It's very hard to measure phase alignment.
I have no idea where you came up with this statement but it is very easy to measure the response of a loudspeaker, both in amplitude and phase.
> If you want to see serious map-over-territory thinking, look at THD specs for amplifiers. It's super-easy to measure THD - just isolate harmonics of a sine wave a 1khz.
THD can be measured at only 1Khz, but it isn't something intrinsic to what 'THD' means. Measuring at only 1Khz is generally indicative of a crappy amplifier manufacturer looking to inflate their power numbers. Proper specs will provide a 20-20kHz THD rating.
> Dynamic recovery behavior, intermodulation distortion, stuff like this is what gives amps their distinctive sounds - but it's nearly impossible to measure!
If an amp has a distinctive sound, it has failed to achieve it's core design goal. I'm not sure what you think is impossible to measure, but I assure you it is not.