We nearly always turn the pump off when not in use.
Agreed on the water heater being full of water comment. We also keep it turned off when boon docking and only turn it on when we need actually need hot water. On gas the water heats up in minutes anyway and avoids problems like using propane for nothing or having one of the kids leave a bike or similar too close to the exhaust vent etc.
2016 Jayflight 26BHS Elite
2014 F150 4x4 Super Crew, Eco-Boost, Max Tow
Bayliner Trophy 2002ff