No, I get that and I think we are in agreement.
I would just highlight that this subjectivity applies not only to the headphone but to the recording and to music itself. Two people might sit next to each other at a concert, one having the time of his life, the other completely unimpressed.
However, the goal of the headphone should be to reproduce sound as faithfully as possible and leave the creative part to the musician, producer, etc. That's why I think it's possible to say that headphone A is better than headphone B (yes, based on measurements, not auditions), because its mission is purely a technical one. Not as easy to do with musician A and musician B or even recording A and recording B, because the artistic side comes into play and that is very much subjective.
That is at least my vision. Some headphone manufacturers (if not all) are trying to play artist themselves and add their own flavor to the sound reproduction. In a world where all headphones are equally far ("far" criteria to be determined) from the reference, they are all equally good and subjective assessment is all that we have left.