The driver parameters that change measurably after break-in, to the point that it is audible. The manufacturers typically rate (higher end) electronic components used in crossovers, at 5% tolerance. The latter also drift with burn-in. The latter is also claimed by some to be audible.
It begs the question: When there is such a measurable variance and corresponding audible change in sound, why do speaker manufacturers not sell premium or ultra premium products advertised as "Already broken in, the sound quality you hear today is what you will hear for life"? You don't see Monoprice or BJC, nor Dave (Ascend) or Dennis (Philharmonic) or Brian (Rythmik) or Tom (PSA) doing it. Fry's doesn't stamping burn-in times on their electronic components.
Surely, there must be a market for speakers in which every driver is broken-in and every electronic component hand picked to offset tolerances and give a that much more predictable speaker characteristic. Paradoxically, the higher end one's purchase, more likely one is to be advised a burn-in/break-in period! How is it that not a single manufacturer at any price point finds value in this?
I conjecture, the extra effort does not yield that much improvement over "eyeballing" everything to ensure the complete package meets an intended specification within the total package tolerance.
Further, if there is no price point at which a speaker designer/manufacturer can prove audible improvement from using burnt in drivers, electronic components, etc. there must not be that big an impact when put in context with other things intrinsic to the speaker/package (good design philosophy, using drivers within specific bandwidth, phase alignment, electronic components within manufacturer guidelines, etc.) or extrinsic to the speaker/amplifier (room acoustics, recording quality, etc.).
So, in closing, if the all reputable designers/manufacturers would rather devote their skill and resources on other things, why should I get hot over burn-in?