Group delay is just another way to look at linear phase distortion.
After double integration the phase distortions are known.
Whitening usually leaves some phase distortion in the results.
The same is true of the absolute phase distortion on each leg (left and right channels) of a stereo pair of lines.
The circular-staircase effect was probably due to phase distortion.
This phase distortion can create the perception of a "ringing" sound around the filter band, or other coloration.
Thus, frequency-selective fading and phase distortion can be easily combated.
It can be corrected with careful measurement of the ultrashort pulse and compensate the phase distortion.
The human ear cannot hear phase distortion, except that it may affect the stereo imaging.
The cost is that this eliminates the possibility of decoupling the spectrum, and introduces phase distortions into the signal.