Interesting observation. An air conditioner (used for cooling) is already a heat pump (moves heat from inside to outside using the compression and expansion of a working fluid, or gas), so no more gains are available on the cooling side other than tiny gains in efficiency from newer compressor motors, etc. Being able to reverse the heat flow for heating (moving heat from outside to inside - what we commonly call a "heat pump" even though an AC only unit is a heat pump already) is great technology. According to the Dept. of Energy, efficiencies up to 300%, in the best cases, may be available. That means that for an input of 7,000 Btus of electricity, you could move 21,000 Btus of heat into your RV.
Even if you had to pay for the electricity at the RV park, it would be substantially cheaper than buying propane. If you have a good sized solar system, it would be free, ignoring the initial cost of the solar system.
Why did I pick 7,000 Btus before? Well, many larger RVs have 35,000 BTU/hr propane furnaces. Assuming a likely 60% efficiency, that furnace can put 21,000 Btus into the RV in an hour. To replace that with a heat pump with 300% electric efficiency would require 7,000 Btu/hr of electricity. That hour of electricity would use 171 ah of 12v battery storage power (7,000 Btus / 3412 Btus/kwh = 2.05 kwh = 2,050 wh / 12v = 171 ah).
We recently stayed in southwestern Utah. It got down to or below freezing each night. We had shore power so the only thing we used propane for was heating. Based on propane fill frequency, we used about 160,000 Btus/day, all at night. At 60% efficiency, we put 96,000 Btus of propane heat into the RV each day. Using a 300% efficient air source heat pump would require 32,000 Btus of electricity or 781 ah of battery storage at 12v, each night, just for air heating alone. We also ran the electric fireplace and a small electric oil-filled heater a lot so I am significantly understating the battery storage that would be required to replace propane if we had used propane for all the heating.
If you have a power hookup, all this in irrelevant. In fact, I plan to install an electric heat option to our furnace to eliminate the use of propane when hooked up. If you are boondocking in colder weather, you would need a good sized battery bank, particularly if you have any overcast days. Also if you are bookdocking, you would have to add in hot water, refrigerator, lights, cooking, and all other power uses into your power consumption. Needing a 2,000 ah battery bank would not be unreasonable for an all electric RV in a cool but sunny climate. An obvious work-around to the overcast day problem would be a good sized backup generator, either gas or propane (Oops!).
Water heating as a by-product of cooling the RV is a great idea. Water heating as a by-product of heating the interior won't gain you anything as there is no waste heat available. A Btu into the incoming cold water will be one Btu less into the interior air.
A lot of RVers probably don't boondock in cold weather so I think there are a lot of cases where an all electric RV might work, ignoring the cost. It wouldn't work for us.