Your example is good but you’re talking here about modulation which is non-linear process and affects the amplitude (in case of AM) and phase (in case of PM - I think PM is more correct abbreviation rather than FM for the mentioned example)… In this case the ear is pretty well sensible to the change of the phase. When we’re talking about linear processes (which static equalization is) the ear can not say to us: “Oh, this frequency has 0 degree phase shift, and that frequency - +180 degree phase shift”.
That is kind of my point, you can’t just say “ear can’t hear phase,” you have to write a paragraph or more describing the exact conditions you have and why that does or doesn’t apply. Even for linear processes it can depend on the rate of phase change, a very extreme change (which would be difficult to do with analog, but quite possible with digital) can be audible. I do not know all the details, but a simplification would be something like if the phase change occurs within one critical band it can be audible. Since the critical bandwidth of cochlea nerves varies with frequency that is not a fixed bandwidth in Hz.
But all that is mostly academic. Any real physical process which changes frequency response (like a resonance or high frequency roll-off in a speaker or microphone, or even a vibrating panel of an instrument) is going to have an associated phase shift, so phase shift in analog or IIR equalizers sounds “natural” in that sense. The requirements can be different if you are trying to design the complement of some existing process (e.g. a filter in a crossover to correct a resonance in a speaker), but assuming we are talking about artistic manipulation when mixing recordings, as Duke Ellington said “If it sounds good, it IS good.”
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