Why I love my modded KEF Q100 speakers? Thanks to a very good 5.25" coaxial I have time aligned ALL frequencies ->"magical" sound versus traditional 2-ways (KEF 6.5" coaxial has not these "magical"). With acoustic instruments the "magical" is more great.
The problem with the delay is if they are different in woofer versus tweeter, like 2-ways.
https://en.wikipedia.org/wiki/Loudspeaker_time_alignment
[ Loudspeaker time-alignment usually simply referred to as "time-alignment or Time-Align" is a term applied to loudspeaker systems which use multiple drivers (like woofer, mid-range and tweeter) to cover the entire audio range. It is the technique of delaying the sound emanating from one or more drivers (greater than 2-way) to correct the transient response, improve accuracy and, in non-coaxial drivers, improve the directivity or lobe tilting at the crossover frequencies. ]
In class A and AB, the phase is not exceeded by +/- 6º in the audio band, although it is rarely publicized. Why should class D have another criteria?
https://www.audiosciencereview.com/...-of-purifi-1et400a-amplifier.7984/post-254975
Hypex NC400, measured by amirm at my request. The graph shows how the phase varies with frequency, progressively, but varies.
Of course, loudspeakers with a good DSP you can solve the problem -> Kii and many others. But traditional loudspeakers without DSP...
Phase is important for crossovers in speakers. Poor phase alignment causes summation issues and directionality issues as you show. Do not conflate this with unrelated amplifier issues.