Some say, and it makes sense to me, that the fibers of the cone need to break down a little bit. This would ostly happen near the voice coil, where cone stresses are highest. It would provide a little treble reduction, and some damping of resonances - the latter would be especially important for a raw FE166 or other whizzer-cone driver, since the whizzer gets no resonance damping at the outer rim.
I'm sure you could get an argument going on other forums about this, I don't think it's universally accepted. But I believe I first heard of this from Terry Cain, who also said that cryo treatment was worth around 500 hours (IIRC) of break in, but had the disadvantage that half the time the magnets would fall off. :^) Maybe Clark would remember better?
If this theory is accurate, then it's the same as with spiders and surrounds, you need to give the cone enough movement to exercise the mechanical parts. For suspension parts, it's going to be displacement (low frequency energy); for the cone itself it will be acceleration (high frequency energy). So it should be excited by a broadband source with a similar spectrum to the end use, i.e. music is an excellent choice.