I thought lets look at the instructions, so selected one at random, two items need considering, one is it says room must be 4m³ think on the edge with my caravan, also not against walls and furniture that should be OK, but if used on business premises, and the caravan park is a business, then must be tested once a year, the old PAT testing thing.
I think they should be reasonably safe, however there is clearly a cost involved, and I would expect to have hook up to keep battery charged is far enough but heater may be another matter.
I am not even sure about battery charger unattended, I remember walking past my caravan one year and smelling a cooked battery, clearly one cell had gone short circuit so it was over charging the rest of the cells.
I note our caravan seems to get a damp toilet and shower area, we don't leave cloths in the caravan and we use one of those bags which are suppose to remove damp, I think lack of heating in that area is the problem, moisture goes into the air in rest of caravan then condensates out in the loo area as so much cooler, there is a duct to outside to heat awning, but not one to heat loo.
I have in the past forgot to switch off the fridge, and I think that tends to be enough to dry the caravan. I would be reasonably happy with built in heater set to 500W in caravan with a low thermostat setting, but oil filled radiator if thermostat sticks could be using 2 kW, that is rather a lot of heat.