Originally Posted by Chrisbrock
So the WH is cooled by the water.
I'm not sure what you mean by that. I guess the water does "cool" it, but that is not what I meant.
What I warned against is running the electric water heater without water inside as even brief operation of the electric element without water will burn out that element.
Generally not an issue if you are always using it and hence always have water in it. Highly unlikely the water would just drain from the tank so leaving it on is not really a problem.