For several years we have been measuring loudspeakers and components for design programs like "Ease". These measurements have shown that the acoustic center of a horn is a couple of inches up the throat. The exact distance depends on the horn and throat. In addition, the acoustic center of a constant directivity horn changes slightly with frequency. This is not a real concern when working with one frequency at the crossover point. Your description of the woofer is interesting. Not exactly what we have measured, but interesting. It is true that woofers will lag behind HF drivers due to their mass. The larger the woofer, the more they lag. This also means that smaller woofers have little lag and not really a consideration.
Alignment of a loudspeaker is about aligning the components. Although the listening position is critical for stereo imaging, once the loudspeaker components are aligned, they are aligned at 2, 20 or 200 feet away. Home hi-fi folks are encouraged to align at the listening position.
Where to start here . . . Yes, audio waves can be reconstructed with the components connected with opposite polarity. Please try and review "polarity" versus "phase". These are not the same. Connecting the drivers with the same polarity does not necessarily put them in-phase. In-phase, or aligned, means the signal generated by the two components reaches the listener at the same down point in playback time.
Most Altec loudspeakers with passive crossovers have the HF polarity inverted to put them in-phase. This correction is needed because there is a phase shift introduced by the crossover (all filters cause a phase shift and a passive crossover is a filter). Add this phase shift to non-aligned components and inverting the polarity often puts the system closer to in-phase.
Not sure what power response has to do with phase and alignment. Certainly as more and more power is applied to the components they will begin to react in a non-linear fashion (lagging behind). This problem is not automatically the crossover's fault.
It is a common belief in some circles that crossovers are a bad thing. This concept leads some folks to running their systems with bare minimum high-pass filters on the tweeter and letting the components overlap. Starting from this concept can get you to this statement; ". . . possible sonic effects due to the signal having to fight its way through all those parts. No free lunch!" I suggest that the comb-filtering caused by the overlap is much more damaging then the crossover.
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