BS, it absolutely does not cost you more energy to turn your tube amps on an off relative to leaving them on all the time. Tube life is shortened but not as dramatically as you would think. I do know some people who keep them on because they hate waiting for them to warm up. They are also filthy rich and could care less about tube life. Some tube units like my ARC phono amp have low power standby modes. I do leave that on continuously. I have a class AB SS amp in the workshop that I leave on all the time but the JC 1's in the main system are turned off.
Turning the tubes on and off stresses the filament due to expansion and contraction of the metal with the extreme changes in temperature. Same for transistors although the temperature changes are not as extreme.