what does burning in actually do anyway.
with speakers you have big cones, maybe they are slightly stiff when new.
but with headphones according to google
I think it's pseudo-scientific reason with no evidence than someone posting they think it sounded different after doing so.
One of my favourites passages about it:
Then there are popular websites, which shall remain nameless, that purport to do rigorous testing on earphones and include burn-in times in their routines. You might as well be kissing each earpiece 50 times to see what sonic difference that makes.