There seems to be a lot of confusion in here.
I studied electronics and never heard of any electronic component needing a "burn-in" period except very old stuff. Some equipment that deliver a lot of heat might need to be run gradually for a certain time at first so the sprayed-on protective layers evaporate a bit or perhaps to help thermal paste set in, thus letting heat escape better (yea, mostly sound systems of old... don't know about the recent stuff) Also, most electronic boards that run at a certain temperature can give off a certain typical electronics smell at first (mostly due to the protective layer evaporating) and that smell will go away with normal use. I have heard people wrongly call that a "burn-in" period. BTW, speakers and headphones are electro-mechanical devices, not electronic, and therefore obey different laws. (sorry for bringing that up again, but I had to say it)
It is possible an LED could change tint, but that will also happen with normal use. All electronic components that deliver a lot of heat will have a slight change in characteristics at first (as in input voltage/current current, but mostly output, both of which could affect the spectrum delivered by an LED to a certain degree) and lose power over time (mostly due to heat and sometimes because of high currents), but that will again happen with normal use. There is no need to burn electronic components in; you're just shortening their life for no reason. Also, LEDs do emit a bit of UV light which could affect the phosphors used and therefore affecting the tint, but that would happen over years if at all.
BUT... The original question was about LED drop-ins... If it is true that some need a burn-in period, I suggest that perhaps running them for an extended period of time at first helps expand the outer casing, which is made of softer heat-dissipating metals and let the drop-in take the shape of the host for a better thermal transfer? If that's the case, a specific range of runtime should be used: not too short else nothing will happen and not too long since the heat dissipation is not optimal yet. Gotta be a pretty hot drop-in, though...
