It's extremely important to differentiate between change in properties through wear, and change in properties through short-term destructive use, against change in properties through aging - they are most definitely not the same.
Take, for example, a steel cantilever beam put through repetitive loading/unloading cycles at a high frequency and with a constant (but different in my different examples) load.
1. If the hypothetical load on the beam results in a maximum stress below the fatigue endurance limit on the steel, the beam can undergo (essentially, this is an area of science still under investigation) infinite loading cycles without change.
2. If you increase the load so that the maximum stress is above the endurance limit but not so high that the beam will bend, in a finite number of cycles the beam will eventually break from fatigue failure. This happens at an increasing rate, in that microscopic cracks in the material expand as a result of the high stress concentrations at them, and as the area of the crack increases the stress concentrations increase even more - until a critical point is reached and catastrophic failure occurs.
3. Increase the load even more so that the beam will bend but not break and you will have exceeded its yield strength, strain hardening the (now bent) beam and quickly and permanently changing its properties. It will still spring back somewhat towards its neutral position, but not all the way. After strain hardening, it is now stiffer (at least at the strain hardened area) and will not bend as much under a given load.
4. Lastly, you can increase the load so high so that the beam just breaks (after bending as the load is applied); exceeding the ultimate tensile strength (UTS).
5. Note that all of these are different than just "aging" as a process only dependent on time and the environmental conditions. A steel cantilever cycled below its fatigue limit would last an infinite number of cycles, but if it rusts and fails from that, it's an entirely different process causing failure. Same goes for plastics out-gassing, etc.
Compare to transducers - as far as burn-in is considered, we are not worried about 1, 2, 4, or 5. 1 results in no change, 2 and 5 result in changes that are constant throughout the use of the driver, and 4 results in failure of the driver. So that leaves us with 3 (plastic deformation, from exceeding yield but remaining under UTS) as the only plausible way a driver changes (mechanically) in a manner similar to that of "burn-in".
Now, the materials used in drivers and suspensions are not perfectly uniform - there are some small-scale variations where some sections are under local pre-tension while others remain untensioned or in compression - so even if the driver/suspension as a whole doesn't exceed the material's yield limit, you may see small-scale plastic deformation. Larger-scale plastic deformation, on the order of the entire driver, would be much larger in magnitude and thus much easier to measure.
The problem I see with burn-in is that it is described as occurring at a large initial rate, slowing down over time until it levels out and is progressing very slowly, approaching "no change" over time.
My understanding of plastic deformation doesn't explain if (or how) plastic deformation continues to happen with repeated loads at the same level - as far as I understand it, no additional plastic deformation would happen without an increase in load. This would support some manufacturers' claims that burn-in is instantaneous with the first time a driver is run-in. But I'm not an expert on plastic deformation, nor am I an expert on polymers and their unique properties.
Anyway, my point is that if any change in burn-in happens, you would be able to measure it in driver compliance and displacement for a given voltage. This makes sense - duh - because all the sound produced by driver is a result of displacement of the driver. I know another member here had begun preliminary testing of drivers for this.
So beyond all this, as others have said on top of (A) determining the measurable degree to which burn-in happens and (B) the mechanism that causes it, we need to explore (C) the actual audible impact. Tyll has done pilot studies on (A) and (C) of these; further investigation is definitely warranted based on his results.
Hmmm.... I see potential for another master's thesis...