We boondock a lot -- so we try to be frugal with all of our consumables. It is not a question of money. It is a matter of extending our ability to stay off the grid for long periods of time. So to conserve propane, we turn on the water heater in the late afternoon, when we get home from our hike. Then it is time for adult beverages and snacks, while the water heats up, followed by a shower. Then we turn off the water heater. There is still enough hot water in the tank to do the dinner dishes.
And of course, we turn it off at night -- otherwise, it cycles on and off a few times during the night, and the noise wakes me up.
But if conservation of resources is not a significant concern, then you could certainly leave it on all day, just like we do at home.