If you place an obstacle in front of the driver which has similar dimension to the magnitude of the radiated wavelength you get reflections and diffraction creating secondary radiation sources and discontinuities in the radiation.
https://heissmann-acoustics.de/en/kantendiffraktion-sekundaerschallquellen-treiberanordnun/
The above 0° and 45° are EQed as a compromise in the passive crossover but even there it is already obvious that the directivity is far from perfect having a big step above 3 kHz:
View attachment 161295
Unfortunately the only Geithain loudspeaker with detailed 3-party measurements are 3-ways but even there you see the discontinuities of the pure driver responses
which need some significant EQing even in their passband
and not perfect radiation patterns
Sources of above measurements:
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This doesn't mean that I don't like Geithain loudspeakers, they have excellent tuning and their 3-way 901K and 921K are some of the nicest sounding loudspeakers I have ever heard, but still physics cannot be ignored, there is a reason that companies like Genelec and KEF do a huge effort to design their coaxial drivers instead of just placing a "tweeter bridge" in front of the mid driver.