Aside from the question of repeatability and accuracy of such recordings, I'd just like to say from my own experience that the brain can get used to pretty broken FR curves in a pretty short amount of time, as well. As long as it's not extremely broken, I always go for a headphone because of technicalities over tonality/timbre. Of course the big problem is that "technicalities" is an extremely vague term and things like soundstage is incredibly elusive in terms of measurements and repeatability with FR adjustments (although FR greatly influences it, for sure). I never really go for flat or "dead neutral" tuning, whether it's harman, DF, olaf's own whatever-the-hell-he-uses or whichever. I just get used to the headphone and I'd just fix something if it's incredibly broken in EQ, not to fine-tune really.
I don't know if other people don't really accept the new headphone's frequency response as natural as much as I do or if they swap like 5 headphones between a listening session, but I tend to buy one set of headphones and one set of IEMs, get used to the two signatures and call it a day.