The Reich video was I believe an artificially extreme demonstration. This is so typical of advertising departments.
You don't need to look very hard to see the ground over which the jockey wheel was being demonstrated had been prepared and made very soft, but importantly the ground over which the caravan wheels were being driven was firm.
What it didn't show was how the caravans main driven wheel would cope with the same soft ground, and I suspect the caravan would have bogged down. So has softness of the ground for this demonstration been taken too far?
So whats going on? - The solid tyred jockey wheel is quite hard and does not conform very well to the ground. This means it has a small contact area, and that creates a high contact pressure with the ground. High enough to overcome the grounds structural strength causing it to sink. What is needed is some way of reducing the tyres ground contact pressure.
Ray S's solution is one way. He reduces the load on the jockey wheel by adding more ballast behind the main axle.
But another way is to make the jockey wheel tyre more compliant so it spreads its load over a greater area thus reducing the contact pressure. This is pneumatic tyre solution.
The relationship between Load, area and contact pressure is simple;
Load = Pressure x Area,
and for this purpose we can assume the inflation pressure will be the same as the contact pressure, all rather handy.
So if the load is fixed, then by changing the inflation pressure the contact area of the tyre will change. You reduce the pressure to increase the contact area
Now you may think that adding a second tyre (a'la Reich) must be better, well if the inflation pressures are the same as the single tyre, then the total contact area will still be the same It just means that each tyre will carry half the load with half the contact area. But critically the contact pressure on the ground will remain the same. So there is little advantage to a twin wheel approach. This suggests that Gabgrandad's comment may have considerable value.
To make the twin tyre arrangement work twice as well as the single pneumatic tyre you must only inflate the dual tyres to half the pressure. But this begs the question, Would a single pneumatic tyre at half pressure perform just as well as the twin?
In reality its not quite as simple as I have made out, there are other factors which would favour a twin wheel over a single. For example the shape of a tyre does not exert a constant pressure to the ground over it entire contact area. The shape of its walls will affect how the tyre tries to climb over the next section of ground.
But coming back to point I made above, if the ground demonstrated could not support the caravans main wheels then the twin jockey wheel has no practical advantage.
Pragmatically, caravanners have managed up until now without the twin jockey wheel, is it another product looking for a problem?