There are 7 pages in here (Start at page 1, and pg 2 and pg 3 shows step response.):
Fig.11 shows a good step response produced by a time-coherent, three-way loudspeaker, with the outputs of the three drive-units adding in-phase at the microphone position. There are not that many speakers that produce this good a step response. Of the speakers I have measured for Stereophile...
www.stereophile.com
I've read that.
Did you read page 4, where he quotes Toole: "The advocates of accurate waveform reproduction, implying both accurate amplitude and phase responses, are in a particularly awkward situation. In spite of the considerable engineering appeal of this concept, practical tests have yielded little evidence of listener sensitivity to this factor...the limited results lend support for the popular view that the effects of phase are clearly subordinate to amplitude response?"
And then JA adds: "This is also my view. Of the 350 or so loudspeakers I have measured, there is no correlation between whether or not they are time-coherent and whether or not they are recommended by a
Stereophile reviewer. However, I feel that if other factors have been optimized—on-axis response, off-axis dispersion, absence of resonance-related problems, and good linearity—like a little bit of chicken soup, time coherence (hence minimal acoustic phase error) cannot hurt. In my admittedly anecdotal experience, a speaker that is time-coherent (on the listening axis) does have a small edge when it comes to presenting a stereo soundstage, in terms of image focus and image depth. But time coherence does not compensate for coloration, poor presentation of instrumental timbres, a perverse frequency balance, or high levels of nonlinear distortion."
So a "good" impulse response and a "good" step response are relevant only insofar as they yield a good frequency response (since they're related by Fourier transforms.)