It's not an illusion, it's the absolute width of the stereo image as produces by the drivers. If you listen to a track that hard pans channels to 100% left or 100% right like
old Amiga game soundtracks or early Beatles mixes, you can clearly measure the distance of what you're listening to. It lines up with the distance between the drivers as they sit on your head. Setting aside subjective interpretation, a Sennheiser HD 600-series and HD 800-series will output these music at the exact same points of 10 inches. No "illusions" involved.
You are saying (1) that binaural recording produces the illusion of elevation and distance (which I can clearly hear on my ATH-R70X in your binaural test) and
(2) that there is no such thing as soundstage. Huh?
Because the binaural recording isn't an "illusion", the effects it produces are clearly measurable and will show up on a spectral analysis. It's the exact same reason why a loudspeaker measured with a regular mono microphone will show a flat, downwards slope, but when measured at the entrance of an ear canal will show that large 1kHz-4kHz hump. The human ear filters out frequencies differently than a flat-measuring microphone, and it's those frequencies that create "front, "rear", and "elevation" cues.
Soundstage is the illusion, the interaction between the recording, the headphones (drivers, pads, fit) and your incredible perceptual apparatus. It's not the distance between the drivers.
It's also something that's way too subjective and immeasurable to be used as a serious recommendation for newcomers compared to the frequency response measurements, build quality, comfort for long-term usage, any quality of life features like detachable cables or a built-in mic etc. To your ears, you hear headphones as a massive symphony that fills the room around you. To my ears, I hear both the Sennheiser HD 600 and Sennheiser HD 800 as just a plain, 2.0 channel signal being played back from drivers a few inches away from my ears.
a) Frequency response curves do not capture tonality and timbre.
I disagree, I find the quality of "timbre" to be severely overstated. It's just an acoustic voltage being played back on some magnets, nothing at all like whatever drum analogy you came up with. Engineers like Sean Olive have done tests between real headphones and virtualized headphones using EQ translations and found an agreement of 85% confidence between trained listeners. Maybe in exotic cases like some boutique estats you might find timbre differences, but not for the dynamic drivers that make up the majority of the market share.
b) Why would you want to equalize to the same target?
Because the Sennheiser HD 800 sounds like total garbage out of the box? It's basically a $1500 Philips SHP9500 without EQ.