The one time when I heard the most change due to burn-in was when I put the headphones and a music player in the closet for several days.   So, no possibility of "brain burn-in"...

So, it's clear what parts wear in engines and sneakers, and why.  So that we can make the connection with headphones... which parts of your headphones are wearing, and how?

That's discussed in both the links.

Mechanical wear is so obvious when discussing things like the modulus of change in elasticity, it's amazing to me such things are even questioned.  A lot of real effects are simply criticized because of who or the way they are presented often by nutjobs.  The degree to which anything is or can be observed depends on many many factors.  I've heard phones and speakers with no audible change, positive change and worse change.  Just depends on things like construction and design.

Where I will go out on the line with subjective experience is capacitor burn-in and wear.  This is much more difficult to study as it's both a chemical and mechanical effect with often more nuanced effects.  People will argue that caps of the same values will sound the same regardless of construction but they have obviously very little experience.  It's very easy to find two caps with the same voltage and capacitance ratings that sound night and day from each other.  So dealing with those folks as chemistry stabilizes or a cap dries or wears out without sufficient interwebz data is like pulling teeth.

I don't doubt that loudspeakers (large woofers specifically) can undergo burn-in. But where is the data that points to headphones undergoing such drastic behavior?

Are you suggesting they can't because they are mechanically the same as a woofer but just smaller?  What quantum physics are you citing that mechanical and chemical change no longer occur once they reach a certain size?

The better question I think is in regards to the degree of audibility and audio measurements.  It's a better case to say that mechanical change in headphones is less obvious or inaudible due to the smaller drivers having less mass and smaller excursion, thus the range within which audible change can be perceived from potential wear is much smaller.