Doppler distortion obviously exists. The question is one of how audible it
is.
My feelings are "not very." You don't hear people who own full-range
electrostatics complaining about Doppler distortion.

Consider the following. Suppose an electrostatic speaker is reproducting 60Hz
at
a peak-to-peak excursion of 0.25". That means its maximum velocity would be
around 30 inches per second. That's less than 1/4 of 1% of the speed of
sound!

Right, but this is a speaker that has a huge surface area and therefore has
a very low total excursion. This is a _good_ thing. When your woofer
excursion starts getting to be an order of magnitude larger, the numbers
change. But the large surface area of an electrostatic panel means you can
get considerable bass without substantial excursion... which is good because
nonlinearities in the field become a big issue when there is substantial
excursion.

All correct, but multi-way dynamic systems with such large excursions eliminate
much of the potential for Doppler distortion, simply because the higher
frequencies are reproduced through a separate driver.

Note, also, that such a large excursion would usually occur on a bass transient,
not during "normal" (???) music.