Every single component, no matter what, benefits from break-in.
Every single active component, no matter what, benefits from either leaving it on all the time, or having it warmed up sufficiently.
Every single person who disagrees with that is certainly welcome to his opinion, but benefits from a real life example of the above, no matter what.
Every single person who can not hear that difference, no matter what, should maybe look either to a different hobby, or stop obsessing about it.
Every single customer of mine, no matter what amplifier, had a "aha" experience with break-in and warm up.
Now, of course it is best to leave any component on 24/7 unless the manufacturer tells you different.
I am also aware that there are a lot of people who don't feel comfortable with it, and prefer to turn the system on and off. No argument here.
It is hard to put exact #'s and scales of improvements of the differences. Each system is organic, and each listener has different habits, abilities, and also seriousness about this hobby.
However, as for our amps, I would say that if you do casual listening, who cares ? For serious listening, expect at least an hour before the amp starts opening up again. Discharge time is usually 30 minutes +.
For total recovery of the last ounce of performance, you're looking at a couple of days.
So, having this out of the way, the question remains as to why there is such a big difference (to many) between different amps and their obvious different warm up times and severity of improvements. Well, you can spin it any way you want to. Up to you.
As for me, I would say that after you have broken in the amp (that , however, is mandatory to achieve best sound) and even stone cold, the Khartago and the Stratos is one hell of a piece, that only gets better by the minute.
Have fun,
Klaus