As RogerL has stated its question of what power is available, and without doubt the limited 16A mains supply would not be enough heat the water demanded on a continuous basis.
There are also historic technical reasons why gas systems were not available to produce instant hot water in caravans. In the distant past there were instantaneous water heaters in some caravans. These were technically like the old fashioned Geyser water heaters with used direct water heating with an open flame. These were outlawed for safety and efficiency reasons. Having an open flame and the way they burned meant they produced unsafe levels of carbon monoxide and dioxide which were able to be vented directly into the caravans living space. They also used a lot of gas which meant the volume of the flue gasses would easily begin to overwhelm the caravans limited ventilation. Such types of heater were made illegal as all dedicated gas room or water heating has to be room sealed which prevents any flue gassed entering the living space of the caravan.
The second reason was legislation that directed all gas appliances must prescribed levels of energy efficiency, and geyser type heaters were not able to guarantee they could maintain the required thermal efficiencies.
I know from personal experience how difficult it is to design and engineer high capacity gas burning systems that can operate in a small space, and the caravan manufacturers of the day were not prepared to entertain a heater that took up more physical space, so the development of instantaneous water heaters for touring caravans was not economical.
What changed the game was the introduction of Alde heating whose vertical form factor can bee better accommodate the necessary heat exchanger size and shape to enable higher gas capacity burners to be used.
