I wondered the same thing. Unfortunately, the hot water element is directly wired into the coach, so I could not measure this using my Kill-A-Watt.
However, one evening, I pondered the question. We sit, unfortunately now much longer, for a couple of weeks to a month at a time. When the meter is running, and I pay for electricity separately from the rental, I calculated that turning the electric element on, and off, is much cheaper. Cheaper than even propane.
The answer to your question is; IMHO, using my scientific mind, turning off the electric water heater when it is not in use is much cheaper than leaving it on all the time, even calculating in the time to bring the water back up to 120 deg.
07 TM 40D;ISL 450 Cummins(upgraded). Very happy w/coach
Gnarly toad to scoot around.
Geocaching, hiking, fishing, National Parks, Civil War sites.