If all goes well, there's nothing strictly wrong with letting a tube amp idle all the time, except that you'll technically be using hours of the tube filaments' lifespans, and causing your electric meter to spin for no good reason. Some tube-based military radio gear like the
R-390A was left on 24/7 to maintain stability, and they generally were very reliable. Also, as others have said, turning them on and off all the time has its own negative effects; early tube-based computers like
ENIAC had issues with tube filaments blowing out all the time until they started leaving them powered up for long periods of time. Obviously, they could afford to pay the high electric bills associated with doing so..........
However, if things don't all go well, you could experience a meltdown. This past fall, I powered up my
Dynaco ST-70 in preparation for a listening session, and then called a friend on the phone. A few minutes later, while chatting with said friend, I heard some odd crinkling sounds from the ST-70, which was sitting nearby. I looked at the ST-70, and one or both of the EL34s in the right channel were red-plating!
I quickly hit the power switch to turn off the amp; if I hadn't been in the same room, the tubes might've melted down, possibly taking one or more of the transformers with them. Since then, I've been very careful to not leave my vintage tube amps sitting unattended for long periods of time.
-Adam