I frequently ask myself how this type of legend starts. A lot of these "things" often comes from real phenomenon that are misunderstood (or squarely lied about!) or applied in the wrong context. Human psyche does the rest...
The one for electronic break-in could be an extension of the very real electronic "burn-in" tests where electronic is challenged (hot room, loads of power...) to age components artificially to weed out early-failures components (the vast majority of electronic components that fails will fail within six months; most of what survives that period will survive a long time). It is possible that some individuals throughout modern age have confused the purpose of the natural-selection burn-in test and extrapolated a required "break-in" period that would logically continue to "improve" while the only thing they are doing is further aging their equipment and reducing its life expectency.
As for Axiom (and if my memory serves me right), their burn-in period is 100 hours at at least 400W (M80s). I don't remember exactly (nor the details) where I got this; could be from a reviewer that had done a tour of the facility or Ian answering someone in this forum. If after that the speaker still needs "break in", return the speaker!
