So who here listens to square waves
Please raise your hands 
I remember maybe a decade or so ago that there were lots of claims made about response to square waves and many graphs. Often eStats had a better match to the square wave input than dynamic drivers which doesn’t prove a whole lot.
Square waves are a very common waveshape for synthesizers in both electronic and rock music. Judging a transducer’s potential by its representation of a steady state square wave would be a bad call for myriad reasons 
Depends what your using the measurement for.
Anyone building an amplifier is going to run a square wave through it to understand it’s slew rate and how it rings, and if that behavior is consistent with changes in input volume. That may or may not be interesting in a headphone driver, personally I’d assume it is until I had evidence it wasn’t, but I wouldn’t assume it mapped to a specific perceptual thing.
I think SBAF did some experiments with similar input signals for headphone drivers at one point.
Measurements more often than not tell you something, the mistake is extrapolating and assuming they tell you more than they do.
It doesn’t miss that though, he mentions it right after the part I quoted from his article, that the exact graph shape you’re going to see will also depend on the performance of your measuring rig.
I did leave this side completely out of my analysis because I wanted to deal only with the concept of ideal response for slam. If you have to drag me over to the practical realm I will say we should strive to realize that ideal response not on this or that measurment rig of course, but at the eardrum – or actually as a devout Sahr-Griesinger-ian I should say at the “braindrum”. 
Neutralize your treble (and mids) according to the Sahr-Griesinger Conjecture 
, adjust the bass to taste/genre and you should be golden… wwwhenever the positional variation isn’t screwing you over too badly. (Griesinger says it worked better for him with in-ears, but I notice what he’s showing in his old video are actually earbuds. It occurs to me right now this probably works better with fully sealing earbuds/TWS that have that bulbous body stopping the insertion at the same-ish depth every time? This should reduce positional variation to the lowest that is possible in any ear-mounted transducer model, no? Hmm… and here I was treating my TWS as the ‘ugly duckling’ of my menagerie, I may have to reconsider that.)
True enough but everyone knows that sawtooth waves sound better.
Here we go, I think I found the better candidate explanation: estats may be sounding strikingly more real not so much because their most planar of all planar membrane movements produce less (nonlinear) distortion but because they produce a closer to perfectly planar wavefront shape, this close to the ear.
Complete Guide To Electrostatic Headphones (With Examples)
Never thought about the wavefront shape, but this makes sense geometrically - if there’s very little to no curvature instead of some detectable curvature, all the little features of the pinna will interact differently and create not only a different overall FR at the eardrum but some phase/group-delay differences too for some frequencies. Seemingly just enough to get people talking about “the sound is materializing out of thin air”, “it’s not coming from somewhere specific, it just gets shot into your brain”. And of course it is, if 1. it sounds like speakers firing at you from infinity (i.e. the distance required for the original spherical wavefront to become fully planar at the pinna plane) yet 2. they have the loudness of something placed right at your ear.
Nah. It’s simple. They just sound better. 