My tube-pre mutes for ~90 seconds on power up and mutes, with a few seconds of delay, before powering off.
The whole “leave it on” stuff is something I hear about all the time, but have never experienced as a sonic bloom of rainbows and unicorns.
But I do leave on the Ayiama and NAD gear that is doing HT… mostly because it is easier for the Haus-boss.
And I would have no issue leaving on the Atmasphere Class-D for convenience sake, but I would not be doing it for sonic benefits.