I think this is a bad idea, but not because of the electrical requirements. Electric water heaters are relatively efficient from a storage standpoint because of the way they can be insulated. So you are looking at saving a relatively small amount of energy by keeping it off most of the time. With a 0.93 EF the losses would amount to about $35 year if left at temperature all of the time. When you need hot water you will have to wait several hours for it to reach temp depending on how long it has been off and the time of year. (The first hour rating assumes the tank is hot to begin with.)
This is info I searched all over for when trying to decide if a tank heater was feasible (vs tankless). I'd spend $5 - $10 a month for hot water at the ready - but not $30-$40 a month. I couldn't find any info on estimated annual electricity usage with zero water demand. Any idea where I can find more details? I'd love to see a guesstimate of energy usage of 50 Gal. vs. 65 vs 80 with zero demand - and at various temperatures.
But the major concern I have is that the water in the tank is going to be stagnant and lukewarm for days or weeks (rather than just cooling for a few hours as timer might do.) It will take a long time for the tank to cool and that will put it in the danger zone for however many days/weeks it takes to cool. If there is any sort of bacteria in the water supply it will have an ideal environment to grow. While I'm skeptical of the legionella concerns at a true 120 F water heater setting for gas, in electric service I would be inclined to run 5 to 10 F hotter, simply because electric recovery times are slow and the tank arrangement appears less ideal for minimizing stagnant low temp zones. What you are planning to do should be nearly perfect for growing legionella if there is any in the supply water.
Very good point. With possibly 3-4 weeks of non-use at a time, I'd prefer not to take the chance. That will save me the money on a separate cutoff switch.
Simultaneous operation will virtually double the recovery time and cut the initial heat up period in half. Keeping the unit on at all times will eliminate the need for simultaneous operation to shorten the wait time - but I still would need the quicker recovery when washing horses or I'll run out of water.
The only chance I have of making a tank heater work, with traditional non-simultaneous operation, is if I increase the size to at least 80 gallons and run it at 145 F - 150 F. But I don't want to spend a fortune for heating hot water during those periods when there is no demand.