Propane or genset for refrigerator when on the road

I run the fridge off the battery when traveling, after cooling it down while plugged in at home before leaving. I don't get the preference for propane. Sure, you don't use that much, but you don't use any off the 12V. I figure I'll just use the propane when I run the furnace (mostly cook on an outside grill) and it'll last a very long time.