If a tank water heater is within the heated envelope of the house, all the heat that "leaks" while you are "maintaining unused hot water" simply goes to heat the house, and your other heat source "runs an equivalent amount less". For example if the heater is in a closet, inside the house.
Since you are asking about electric, be sure to run your numbers comparing what the cost savings would be compared to having a small traditional energy efficient tank heater. In every case that I've run the numbers, there is no savings with electric on demand water heaters compared to the cost of the unit and how long it should last before being replaced.
That is what I was going to suggest. We had one in a Condo apartment in Peru-2 D cell batteries to start the flame. We had 2 of the 100 lb propane cylinders and with just the wife and I, one cylinder lasted about 4 months. It gave all the hot water we needed.I know its off-topic but I've been using this on-demand propane heater at my cabin for 2 years. It's perfect for a shop too. Its 75,000 BTU and has no problem with my incoming water temp 40*F. 75,000 is enough for a shower, we don't mix with the cold (single pipe), and don't run it full blast, its too hot for that. $210, uses gas from a 20lb tank, and no electricity. A wild guess is a 20 lb tank will give 20 good long showers. It uses two Dcells for ignition and its had the same batteries for 2 years. .
Eccotemp L10 Portable Outdoor Tankless Water Heater Eccotemp L1 Portable Outdoor Tankless Water Heater - - Amazon.com
Its pressure activated. You just open the water valve and the flame starts. And you will be a hero if you bring it to Hunting camp.
I've thought about that concept also. Go to the shop turn on the air compressor and hot water reverse the process when leaving.Just a sink in the shop is what I have, and I found a bronze, 2gal tank, AO Smith, 120v undercounter unit that works well for me. I wired it into a switch so I can cut it off when I'm not in the shop for a while. Plenty of hot water to wash your hands or wash out a paint brush/etc.