** But time of arrival for any transient is CRUCIAL !!
You're knowledgeable tons of things, but here you're wrong.
** Phase differences are not heard on headphones at all -- with *SINE* waves.They are. Not only do the books say so -- but I've done the experiment. The ear/brain can hear phase differences -- //steady-state differences// (not just polarity reversals) up to about 1kHz. Not surprisingly, this frequency roughly corresponds to the acoustic wavelength of the head.
You didn't read what I wrote.