Ok if phase is not something we should bother about, and I accept that this may be so, is there then any value in aiming to time align the arrival of bass and high frequencies, in the DRC (Digital Room Correction) process, using whatever methods are relevant?
Thinking that the difference in distance from the listening position, of tweeter and woofer, as well as any timing differences from phase shift introduced by crossovers, may still need to be compensated for, if they are material, to the listening experience.
Still trying to figure out if there is a difference in the timing delay of different frequencies, due to phase shift, and the kind of timing delay that is caused by difference in arrival time of bass and high frequencies, due to measurable difference between the distances from the listener to the tweeter and woofer, for example in a 2 way speaker.
Of the top of my head, my thinking is that the maximum timing delay due to phase shift, will be the time span of a single cycle. i.e. the maximum phase shift will be in degrees 360 degrees. Do let me know if EQ changes such as the kind in minimum phase cross overs (i.e. normal eq either analog or minimum phase digital) can produce phase shifts, that exceeds 360 degrees. If my assertion is true then the maximum timing change will depend on frequency.
Taking a 40hz signal, maximum phase shift here would be 1 second divided by 40, i.e. 25 milliseconds delay. And at the upper end, frequencies like 12k, would have a maximum timing delay of 1 second divided by 12,000 = approx. 0.000083 seconds or 8 hundreth of a millisecond.