I'm not familiar with the science of headphone drivers (or drivers generally), so I can't comment on 'burn-in' of the components.
However, I think it's reasonable to say that the phenomenon of 'burn-in' involves a significant subjective aspect as well, that maybe is just as important as driver burn-in (if there is such a thing according to relevant experts). In my experience, headphones are like glasses (if you have multiple pairs, you know what I mean): the different lens shapes, maybe some lenses are polarized, some are slightly older prescription, etc. If you put them on one after another, they seem mildly different, but noticeably so. But once you wear them for about half an hour, you forget that they felt weird when you put them on.
Headphones are similar. They each have their own sound signature to which you adjust or adapt your hearing, the way your eyes adjust to the lenses in your glasses. You learn how to listen to your headphones, and how to appreciate its strengths and how to reconcile yourself with its weaknesses.
That's all to say that, I think 'burn-in' is just as much a matter of how we adjust ourselves to the hardware we have as it is a matter of that hardware going through a process of well-wearing.