Speaker Break In...? Or listener “Break In”?

I don't hear a difference.  

It's listener break-in. I've done A/B comparisons on identical speaker models before, with one pair being new, out-of-the-box and the other pair being 1, 2 or more years old, with no discernible difference in sound. 

I dont think I've ever heard someone say that the speakers they bought used, do the same thing. In other words, their new-to-them used speakers sound quite different than the speakers they have been using, but they just get used to the sound after a few days/weeks. The speakers were used, so if there was "break-in" associated with them, it would have happened long ago. 

The only difference I can hear consistently, every time, is how my system sounds immediately after start-up and during the first twenty minutes or so. Definitely improves during that time. Have never been able to positively, consistently hear any improvement over hours of use with any gear except my cables and ICs. I also note the system sounds different at various times of the day or night and seems to sound its best on Saturday mornings before 10 AM. 
Not taking sides in this thread, just stating what I've heard over time.
As always, YMMV.
Remember, it's just a hobby, not brain surgery.
Keep it light, keep it fun, have fun, happy listening :)

About decade ago I acquired a thirty year old set of Klipschhorns from a good friend of mine.  Previously I'd been listening to a small set of Dynaudios, which I liked very much.  Upon first listening to the Khorns they sounded harsh to the point that my ears would cringe at certain passages of some of my favorite recordings.  However over time the harshness disappeared and I was able to appreciate the dynamics they were capable of.  Since the speakers were already well broken in, I attributed the change to my ears.  One day I decided to fire up the Dynaudios again, and now they sounded muffled compared to the Klipschs.  Same amp, wires, and music.  This doesn't mean  I don't believe that  some physical break in occurs, just that our minds can play tricks.  Many years ago a piano tuner advised me, "If you keep playing on an out of tuned piano, over time your ears will adjust to that out of tuneness so that when you play on a properly tuned piano, it will not sound right".

Why do some driver manufacturers recommend a "burn in" period. Say, 20 hours continuous music a low level?  Varnish on the cone? 
My own experience in 30 years of working on professional broadcasting equipment, is that the ear adapts to accommodate different loudspeakers.