[marcan_42]

Anyone can hear phase discontinuities because any phase discontinuity is just a burst of high frequency content.

But typical reflections off of surfaces are largely linear as far as I know, and any linear operation will not introduce any power spectrum changes that are phase dependent. As far as I know, the the ear canal can be largely modeled as a linear system (to within the thresholds of hearability).

The only way to hear phase is to introduce a nonlinearity. That then generates harmonics (or sometimes even lower frequencies), and their power spectrum depends on the specific phase relationships of the incoming signal.

A physical example of a nonlinearity would be a vibrating surface that hits another surface at a certain excursion. Depending on the relative phases of the excitation signal, you can have different peak excursion, and therefore clearly get a different result if one phase set makes it reach the other surface and another one doesn't.