Most tankless water heaters in off the grid houses are right next to the shower they serve. Even so there's a bit of a lag between when you start the water flow and when the heater fires up, then adjusts it's flame size to match the water flow.
Putting a tankless heater where a typical RV water heater is located, some distance away from the shower, only magnifies the temperature instability because you're also having to deal with the time delay as water travels the distance between the heater and showerhead.
As far as a tankless heater using less propane, this is pretty much a myth. The Atwood tankless heater the previous owner installed in my trailer had a 50,000 BTU flame, almost twice as large as the flame in a typical RV furnace. The Furion tankless water heater uses 60,000 BTUs to achieve it's 2.4 gallon flow rate.
The 6 gallon Atwood tank style heater I bought to replace the tankless water heater uses 8,800 BTUs. Yes, the tank heater takes longer to heat up but because of the way the flame is routed through the tank, more of the flame's heat is transferred to the water.