Remember, all generalizations are invalid, including the one that says all generalizations are invalid. :lol:
I must admit, from playing many, many gigs with my Mark III, that it does sound better after it warms up. It's less "brittle" or "cold" sounding.
Surprise, surprise, the amp sounds warmer after it gets, er, warm!
I often take it off standby after a minute or so, turn the Master down, and let the amp "run" until it's time to rawk.
Having said that, I wonder if it's the other components, as well as the tubes, warming up, too. The Mark III has the cooling fan, you know, so it may be taking longer to warm up, 'specially in ice-cold air-conditioned rooms.
Using standby is important, but not if it mucks with your sound, man!
As always, YMMV.