Doppler has been analyzed both theoretically and with controlled listening tests to be a non-issue. In rooms, doppler effect decreases as you go off axis. Since bass frequencies are omni directional, much of that energy comes from other axis than 0, sharply reducing Doppler. Even without this factor, controlled testing shows that in the type of excursions we have in woofers, it is not an audible concern.I concluded that Doppler is a real limitation, that cannot be circumvented, but is mitigated by using n-ways, n as large as possible.
See AES paper,
THE AUDIBILITY OF DOPPLER DISTORTION IN LOUDSPEAKERS
Roy Allison, Allison Acoustics Inc.
Natick, Massachusetts, and Edgar Villchur
Foundation for Hearing Aid Research
"Although Doppler distortion in loudspeakers has been often
viewed with alarm since Beers and Belar described it in 1943,
the question of its significance in music reproduction has not
yet been answered. In this study the audibility of Doppler distortion
in simple direct radiators is investigated theoretically
(by analogy to tape-machine flutter and by analysis of
listening-room acoustic effects), and experimentally (by double-blind
listening tests). The analysis predicts Doppler inaudibility
for any practical cone velocity, and the experimental results
provide confirming evidence."
Here are some snippets from the listening tests:
"All eight of the judges evaluated the Doppler-contrast pair
of organ music recordings as the same.
Seven of the eight judges evaluated the Doppler-contrast
pair of orchestral music recordings as the same. One judge evaluated
them as different, marking the channel with Doppler as
more accurate."
"
As in experiment 1, a listening jury was asked to compare passages
of music reproduced in two modes, one with and the other without
Doppler distortion.
[...]
"The reverberant-field correction factor that reduces the
amount of Doppler distortion in normal rooms is not operative
in this experiment, since the on-axis Doppler distortion that
was recorded in the anechoic environment is not diluted by any
off-axis sound. "
[...]
"All eight of the judges evaluated the Doppler-contrast pair
of orchestral music recordings as the same.
Five of the eight judges evaluated the Doppler-contrast pair
of organ music recordings as the same, but one of the five
added a question mark on the response form. Three judges evaluated
this pair as different; one of the three indicated that
the channel with Doppler was more accurate, one that the channel
without Doppler was more accurate, and one that neither
was more accurate than the other.
There was no agreement among the three judges who detected
a difference between the Doppler-contrast organ recordings as
to which channel was more accurate, and it appears likely to
us that their responses were determined by a factor or factors
other than Doppler distortion."
So let's not jump on these things without properly reviewing authoritative work already done.