I once had a fitting come loose while I was away from the camper with the pump on. It pumped my entire 33 gallon tank into the cabinet and onto the floor. Now, I always turn the pump off. If I'm on city water I turn that off when I leave the camper for a while.
Yes, I do turn the water off at my house when I leave. I see no reason to leave it on. If anything broke while I was gone I would probably have a huge mess, a dry well, and a large electric bill from the well pump running continuously. I also turn off my water heater and air conditioning when I leave home. I unplug antenna cables from my ham radios and I unplug lots of cords in the shop.
Why take a chance? It only takes about 5 minutes to hit a few valves and breakers.