They might have broadly similarly shaped electrical impedance curves, but the rise is not always at the same frequency, nor by the same amount. And of course the frequency responses aren't the same either. This all means that the effect of this tube amp's high output impedance cannot be generalised for all these headphones.
Reference Audio Analyzer's excellent comparison tool illustrates this. Below are the frequency responses of some of the headphones you mentioned using the FiiO K5, which has minimal output impedance (0 ohm measured by RAA, 1 ohm as measured here on ASR):
View attachment 80955
And here are their frequency responses using the Laconic Lunch BOX HA-06 PRO tube amp (how do they think up these names?), which has an output impedance of 171 ohms as measured by RAA (close to the 188 ohms of the Bottlehead Crack):
View attachment 80956
As is pretty obvious looking at these two graphs, the effect of the tube amp's output impedance is quite different for each headphone, particularly the Focals. Here's just those two comparing both amps together:
View attachment 80959
Here we see a huge increases in bass, and shifting of the bass peak of the Utopia from just over 100Hz down to 70 Hz, completely changing the tonality of the headphones.
Here's the HD800 with the two amps, showing a much broader increase in bass than the other headphones, extending all the way out to the lower mids:
View attachment 80965
And the Beyers, showing not much of a change between the amps really:
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Finally, as a cross-check, just the HD650 on its own with both amps:
View attachment 80970
This frequency response change in the bass matches very well with what Amir measured, corroborating both:
See above. Your claim that the Bottlehead Crack 'synergizes with all high impedance headphones' is not borne out by the above data, even for a small selection of headphones with similar operating principles. To claim that
all high impedance headphones will sound good (even for a subset of people) using this tube amp is ludicrous, because as shown above the changed sound will be different for each headphone, depending on its impedance curve and frequency response.