After all that, I'm still sticking to my guns in that any perceivable changes in audio "quality" can be explained by other means other than the speakers actually improving. I suspect that explanation is largely psychological.
The term "break-in" could be used to describe the softening of the material. But some audiophool has taken it and applied it to a correlation in performance increase. We must remember that correlation does not imply causation.
I don't know if you've read my earlier posts on this topic, but essentially "break in" refers to the resonant frequency of the drive unit falling during the first use.
Depending on how much production testing the manufacturer has done, and depending on the exact materials used, and also on the use during "break in", this easily-observed change in Fs will asymptote after some minutes, hours or days.
None of that is mysterious or beyond doubt. There is plenty of evidence to demonstrate that this happens. I have published some of my own, and so have plenty of other folk.
Of course, a drive unit has many other parameters, but Fs - a product of suspension compliance (and mass) - is a convenient metric to observe. Once Fs has settled, one can measure the parameters of the "broken in" drive unit with confidence.
Once a designer is in possession of all these parameters, an enclosure can be designed around the unit.
The enclosure (hence, bass tuning) will depend entirely on these parameters. Agreed?
So, if you designed an enclosure based on data collected on a brand-new unit, you would end up with a very different enclosure. It would have a different volume, and different port tuning. It would only be the optimum enclosure for the first few minutes of operation.
Or, to put that another way, the box is designed for a drive unit that has been exercised and is performing according to its long-term specification. The brand new drive unit is not going to be a good match for the supplied enclosure. The bass tuning will be incorrect. But once Fs (hence all the other parameters) have settled, then the box and the drive unit will match as the designer intended.
So, by any objective measure, there
will be a performance increase after run-in. It can be measured and quantified. It might be subtle; it might be significant - it depends on the particular drive unit, and it depends on the box tuning. For example, a simple sealed box is fairly forgiving - a ported box could be less so.
How audible it might be is clearly another matter. It's one of those tricky "it depends" problems. But sometimes, it can be heard. Been there, done that.
I speak as an engineer who has experience in this area, and because I know the mechanism, I can speak in engineering terms about the effect. But our audiophile friends lack this knowledge, so of course they will pick words and phrases from their world. And many engineers will be quick to dismiss their subjective reports as "audiophool nonsense", because that's easy and lazy - no intellectual effort required. But while a lot of what audiophiles claim to hear is very obviously the product of an over-active imagination - fuelled by the hi-fi press, marketing material and internet forums - this is an exception. Data exists. It is real. The only variable is the extent to which is can be measured and heard.
Of course, in public, many manufactures will use imprecise language. They have to be extremely careful about what they say, and what they might give away to their competitors and critics - it is an incredibly difficult market for the majority of small and medium-sized companies that make up the loudspeaker market (in the UK at least). These companies are selling products to audio enthusiasts who are largely non-technical, so they must write in a language that they can understand. And what they publish must be perceived to have a positive outcome - primarily it will be intended to reassure their customers in some way. It's not like they are selling test gear to electronics engineers.
And yes, I do agree that there will an amount of psychoacoustics at play as the owner gets used to the new loudspeaker - this is usually the reason behind the claims of many hundreds of hours needed. I said as much in my first post in this thread. This usually happens when someone has made the wrong choice but is refusing to admit it to themselves - a surprisingly common human trait that isn't restricted to audio.