I don't think that's correct to assume (but I'm happy to be corrected in case it is): If the tweeter can't reproduce the frequency, why would that cause IMD? The tweeter is either low-passed in the crossover or acts as a mechanical low pass filter itself here. And frequencies which dont reach it or which it can't reproduce also can't interact with those which are reproduced. They are simply dissipated as heat in the crossover or the voice coil. So no IMD, because tones which don't exist can't intermodulate with others, right?
Tweeters are usually high-passed in the crossover so they don't get over-loaded with too much LF excursion.
A big bass driver HF response tends to be limited by it's inductance rather than cone break-up, as the wavelength of sound is much bigger than the driver.
Mid-range and tweeter drive unit dimensions are generally similar to the shortest wavelengths they reproduce.
Their HF limit is generally set by cone or dome break up, and that definitely amounts to distortion.
It's not
impossible that a tweeter, being pushed beyond it's dome breakup frequency, has less distortion than a ribbon tweeter working
inside it's working range, but I think the likelihood of that is vanishingly small.
Different topic: The "transient response" argument is always weird to me from a logical perspective. We can't hear past 20-ish kHz, because our hearing and in particular most likely the hair cells are not sensitive to those frequencies. They act akin to a mechanical low pass. So, in consequence, the sharpest transient we will ever be able to hear is the gradient close to the zero crossing of a 20-ish kHz sine wave. You cannot logically separate "transient response" from "frequency response". They are inherently the same thing.
Yes, transient response and frequency response are convolutions of each other, but only when the phase response is linear.
If the frequency response is the same and the phase response is different, then the transient response will be different.
Of course this might be what's happening with Googlebot's test - it could be that the DAC output or the speaker response are linear in phase, and that's what's heard.
When you band limit the frequency response of anything, you
always introduce a phase shift as well. That applies to both the limit of LF response, and to the limit of HF response. If either are extended, even to frequencies where you can't hear the sine wave (like Googlebot can't hear over 17kHz) you will still get a better phase response.