frig left on

An RV fridge uses about 4-5 kWh per day, very roughly, depending on the outside temperature and many other variables. For me, that would be somewhere around $300 a year in electricity if I left it on all the time. I don't think it's worth anywhere near that amount of money for whatever small convenience there may be. (If one needs an additional fridge for overflow, it would be fairly quickly cost-effective to purchase a simple domestic compressor fridge and stick it in the garage or wherever; it would pay for itself in a couple years in electric savings over running an RV fridge.)

As far as the fridge itself is concerned, I don't think it makes any real difference. There's nothing in the water, ammonia, and hydrogen gas that wears out with use or fails with non-use. The cooling system on modern RV fridges is cycling on and off (and hence heating and cooling) continually when it's operating based on the thermostat controls, so the argument of avoiding thermal stresses by leaving it on is hardly applicable in my opinion. (It may have held a bit of validity for older fridges, at least on gas mode, where the temperature control is simply a valve adjusting the flame.)

Of course, if you do leave it on, it is important to have the RV somewhat close to being level.