Another layer of complexity. And controversy. Floyd Toole insists that we cannot hear phase. And even advocates of achieving full phase coherence across the audio spectrum have to admit that a loudspeaker capable of that feat can only do so in one listening position. I try to get adjacent drivers as perfectly in phase as possible at the crossover point, not because there are audible benefits per se, but because that's the requirement to get correct summation if you're targeting even order Linkwitz-Riley acoustic slopes. In other words, optimizing phase consistency between drivers is a means to an end, not the end in itself.
And just because two drivers are in phase doesn't mean they're phase coherent. For advocates of phase coherence, the Holy Grail of speaker design is not only to keep the adjacent drivers in phase at the crossover point, but to have them reproducing the exact same cycle. For a 4th order Linkwitz-Riley crossover properly executed on a flat baffle, the tweeter and midrange will be one full cycle apart--they're in phase, but not at exactly the same point in the music. To get full phase coherence will generally require a sloped or stepped baffle, drivers with extremely smooth roll-offs, and probably a very complex crossover that maintains, say, near-perfect 1st-order acoustic slopes over a 2-octave band. And then the off-axis response may be totally screwed up. So--until someone can demonstrate that the benefits outweigh the costs, I'll pass on the Holy Grail.
Of course, all of this just applies to passive crossovers. DSP can dol all this without breaking a sweat. So I guess we should all just grow up and design speakers, or buy speakers, with active digital crossovers. Then we won't have to argue about whether phase coherence matters for proper imaging because we can flip a switch and listen to what happens to imaging with true phase coherence and with quasi-phase coherence. I've participated in demonstrations like that, and I sure couldn't hear any difference. But I'm 200 years old.
