As someone who has built, and rebuilt some amps, I find the idea of an audible break-in, preposterous, past initial warm up, and well into the degradation, end of life period. Why? Because my final bias settings would change, and that could be problematic, especially from one channel to the next. Capacitors, for example, by default, tend to have a margin of error that can measurably vary as much as 2-10%, for even reputable brands. What if all, or most the capacitors, managed to skirt the maximum of that value in one unit? In a mass production sense, that has to happen at least some of the time. In other words, the unit would at least have to be broken-in at the factory.
As it stands, when building, or rebuilding an amp, I only have to let it come up to operating temperature once, for about 20 minutes, to set the final bias settings. Just to be sure, I check them again after it's warmed up and played under load for awhile. I usually give it a week or so on the bench. My settings don't change, provided I wasn't drunk when I soldered the thing up. The pots used to set these values with, are so incredibly sensitive sometimes. Even just relieving the directional pressure from the screwdriver can change it.
What does change? I change. My mood changes and my sinuses due to dust and allergies sometimes, or if it's been a particularly noisy day at work. I can warm up to pieces of equipment as I play them. Sometimes, my sensory attention span is more clear. I have a pair of wide band speakers that are a little thin when first turning them on. After about 10 mins though, they sound incredibly detailed and the midrange, incredibly clear. I have to warm up to something that precise, it seems. The variable here is dependent on how much I am paying attention. It's much less noticeable say, if I am reading while listening, perhaps.
It's not a bad thing to admit 'self' break-in. It happens with the way a car feels the first day you sit in the seat, to a week from then, how food tastes and everything else. Even girlfriends and such, and is certainly more explainable than electronic voo-doo.
