So this thread turned out to be a bit of a car crash. I am sorry about calling burn in 'nonsense' in the original post and anything else that made it appear I was laying down the law for others to follow. That was counterproductive and clearly got peoples backs up. It was also unintentional.
With my limited knowledge I have read through the various tests and the article I have linked to and would, IMHO conclude
- manufacturers themselves do not agree whether burn in exists or not with their own speakers (HifiMatrix article)
- there are mechanical changes with speakers (all of the tests linked to)
- those mechanical changes do reverse to one degree or another after use.
- it is not clear how long the reversal takes. Audioholics and one of Tom Nouaine's tests left the speakers for much longer after use than they were left in other tests. It is clear that the less time between the end of the test and the measurements, the more likely it is to find changes still present in the speaker.
- we need more tests, particularly to confirm whether or not, given sufficient time all speakers will return to their original state after use and with headphone speakers.
- if all speakers do return to their original state after use, there is no burn in as commonly described by the audiophile. But, depending on how often you use a speaker, if it takes a day or so to return to its original state, your use of of it may mean that it never has a chance to return to the original state. So, in that case there is burn in.
- in any case, to what extent are the changes audible, particularly in terms of improving sound quality?