I would agree with you there. Is the opposite really being said?
Whether this is so, I cannot say, my interpretation of statements to coaxial systems about IMD, went (apart from the usual causes of IMD) always toward Doppler effect - but also I can be wrong there with my interpretation.
Whether the "directivity modulation" you describe can be subsumed as IMD is another matter - probably not.
If only a qualitative assessment of the impact is needed, a simulation can give you the answer.
As an example, consider a 1'' tweeter with a "simple" cone of 10cm diameter (roughly equivalent to a 6'' driver). The coaxial system is built into an infinite baffle.
First, we consider the radiation of the coaxial system at rest and then with only +-3mm excursion (cross-section with the tweeter cone and the woofer cone):
View attachment 117549 View attachment 117550 View attachment 117562
Don't mind the 3mm step around the tweeter, it has to be like that (to have a minimum of radiation control at high frequencies, without it the radiation looks bad - but can not be explained here).
Let's compare the frequency responses from 0°-90° in 10° steps:
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To make the comparison easier, we normalize to the axis frequency response:
View attachment 117555 View attachment 117556 View attachment 117568
same as spectrogram:
View attachment 117557 View attachment 117558 View attachment 117569
It is easy to see that even 3mm of excursion leads to a considerable "modulation of directivity".
This should also make it clear that it is not a good idea to design a coaxial system as a full-range - at least if the sound pressure in the bass range could lead to greater excursion of the woofer.