maybe you should get equilibrium for a trial. try something like linear phase filter, rise the impulse length and padding and come back to me about how easy it is to hear phase shifts.
maybe you're exaggerating things, maybe you use an EQ with settings that really make it obvious to hear some ringing, maybe what you call easy is to apply a +15db super steep EQ that nobody would have a reason to use? maybe your experience has nothing to do with music and you just assume that the result would be the same? IDK. but easy to hear, even though it's a subjective thing, I just can't agree with it if you keep talking about EQ as a general thing and it concerns music.
the phase shift is indeed a thing, it's audibility in casual normal use is really a different matter though. at the mastering level it's yet another matter, just mixing 2 tracks of the same instrument from 2 mics has the potential to become a problem(thus different filters to deal with such problems). and as I said before, variation of phase from one ear to the other is a special case, that's where we're really very sensitive to it. while mixing this can have a significant impact. but most sources are in mono anyway. so what we'll get in the end as time delays between each ears will be the manufactured panning. nothing "real" to hear.
you don't have to use EQ if you don't want to, but it's a great tool used everywhere for a reason. if phase shifts were so obvious, then what music are you listening to? how many albums weren't EQed? what will a little more EQ change to that sacred phase that is just the byproduct of mic positioning and mixing anyway?
again there are actual cases even with my own IEMs where the EQ improves the general phase curve. not that I can claim to notice it, but I do measure it.