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Fixing phase shift involves time delay. This makes the diaphragms in the system (again, at the crossover frequency) make the same frequency at exactly the same time, removing the phase shift at the "center frequency", and minimizing the destructive interference (damage) both above and below that "center frequency".
When the phase shift is removed or minimized, this is how you acheive a "perfect" frequency response. The sound power of the system becomes as flat as possible, preventing holes or peaks in the overall response of the system, and I think this is the answer to the OPs "better" question. REMOVING shift (i.e. delay) by ADDING delay (i.e. shift)... It doesn't seem right or sound logical, but that's exactly what is happening.
