Drewan ... IME, as I stated above and/or elsewhere, room EQ what effects cannot be understated ... unless your sound room is an anechoic chamber. I was *VERY* surprised at how my sound room/man cave twisted the mid and bass frequencies in my right front facing speaker. The result was smeared imaging. Didn't appreciate the impact of the room issues until the DEQX effected room EQ.
Time alignment, I think goes more to tonal attributes because the impact of high order x-overs is to skew/jumble the speaker's output signal. See Roy Johnson's White Paper. Having said that, ... perhaps correcting time alignment might have other qualitative sonic benefits too.
Let's face it. Most of the tippy-top big dollar brands on the market are not time coherent, yet people still rave anyway. For example, Magico, Wilson, B&W, Daedalus, and so forth. Maybe if one gets used to sonic swill, it sounds good after a while. LOL :)