Of all the audiophile pet theories, I think the notion of "burn in" is the most inherently misleading. What may not be silly is to believe that any component in the chain, from cap to cable to cone, could have a break-in or stabilization period, and even a measurable one, before optimum functionality is reached. What definitely is silly, is to suppose that the length of break-in time can be detected merely by listening. Say you've just replaced ('upgraded') the caps in one of your boxes. We're supposed to believe, through all the variables one is subjected to in the act of listening to music, not only a) that you picked up the difference between the new caps and the former, without the benefit of an A/B (and maybe you have! it's quite believable), but also b) in the event that the caps, because they're not yet broken in, have in fact made your system sound temporarily worse, that you were not only able to safely ascertain at which point the new caps managed to equal the old ones, but when they surpassed them -- all based on your, by this point, undeniably uncertain memory of how your system sounded before? I doubt it.
In swapping any component, if you don't pick up a difference in the first few seconds or minutes of listening for better or worse, while there may well be some benefit that doesn't blossom till later on, you're kidding yourself if you think you're going to spot exactly when that is. Nobody's aural memory is that good.