If a manufacturer ever recommended leaving tube gear on all the time in order to prevent damage from the act of turning on the gear, I would never buy from that manufacturer. It is not hard for the manufacturer to put in a soft start circuit to prevent damage from turn on. A tube is not like an incandescent light bulb (which is designed to come on instantaneously) and it warms up relatively slowly so that it does not suffer as much from thermal shock of being turned on. There is a potential for damage if the plate voltage ramps up too fast such that full voltage is applied before the cathode has warmed up enough to be fully emitting electrons (referred to as cathode stripping). Cathode stripping is less of a concern if the amp is tube rectified because the rectifier itself slowly ramps up the plate voltage as it warms up. Some amps, particularly those with solid state rectification will have a circuit that limits plate voltage until the cathode has time to warm up (my linestage, although tube rectified, has such protection).
The only good reason to not turn off tube gear when one is not listening to it has to do with warm up time. Tube gear, like all other gear, sounds best when it has been on for a while. The good news is that tube gear usually sounds good within five to ten minutes of being turned on, which is a much shorter warmup period than solid state gear requires. I leave my gear on when I am taking a short timeout from listening, but, otherwise I turn it off, particularly when the gear will be unattended.
The only good reason to not turn off tube gear when one is not listening to it has to do with warm up time. Tube gear, like all other gear, sounds best when it has been on for a while. The good news is that tube gear usually sounds good within five to ten minutes of being turned on, which is a much shorter warmup period than solid state gear requires. I leave my gear on when I am taking a short timeout from listening, but, otherwise I turn it off, particularly when the gear will be unattended.