Leave tube amps always on?

There are ways to gently turn on tube gear, such as a soft-start circuit, relays that apply full power to the B+ rail after the heater/cathode has been warmed up and emitting, etc.  If a particular design is hard on startup, it really should be the designer's responsibility to use such measures instead of recommending that the owner waste electricity, prematurely burn up tubes, or increase the risk of damage to equipment and the home if something goes wrong with an unattended piece of gear.  

Tubes, generally speaking, are NOT like light bulbs, so they do not suffer nearly as much from the thermal shock of being turned on.  While tube gear might take a few minutes to sound its best after being turned on, that time is typically shorter than the warm-up time for solid state.  It really shouldn't be the case that it is better to leave the gear on all the time.

Tubes do not "use" more energy at turn on or turn off.  That is NOT the basis for concern with turn on causing more damage to a tube than leaving it on constantly.  The concern has to do with two different issues.  The first is the stress from thermal shock.  When a cold tube is suddenly heated, the elements that are heated are stressed by the sudden heating and expansion.  That is why light bulb most often fail at the moment the light is switched on.  Tubes are subject to some thermal stress, but, it is not nearly as severe as with a light bulb.  Tubes are not made to heat up and start working as fast as a light bulb has to heat up and emit light. 

The second issue is what is sometimes referred to as cathode stripping.  If high voltage is suddenly applied to the anode before the cathode/heater has warmed up enough to be emitting electrons, the pull of the anode trying to attract those electrons can damage the cathode.

In a properly designed amp, the current should be applied slowly enough, and ideally, first to the cathode/heater circuit, and ramped up to avoid either concern.   Some tube units have such "soft start" circuits and utilize a relay that delays full power to the anode side of the tube.  My headphone amp has a circuit that takes a full minute before warm up is complete and the amp is operational.