Hello Ian,
If you only intended to use an 'A' frame mounted mover at home where you say you have a flat hard surface, then I believe it would be fine. Your last note about using it on sites does raise concern; Most of the other respondents have hinted that their experience with this type of mover leaves a lot to be desired, simply because they become ineffective on uneven, slopping or slippy surfaces.
It is down to basic physics, that the maximum push or pulling force (drawbar) one of these devises can produce is only equal to the force (or weight) pushing the driving wheel to the ground. In most cases that will be the nose weight of the caravan plus the weight of the mover circa a maximum of about 125Kg, and could be a lot less. That would be about equal 1.5 adults.
Now consider; How much of a slope could two adults hold your caravan on without the brake? Not very much, and the a frame drivers suffer exactly the same force so that is a major limiting factor.
From a safety point of view. If you were manoeuvring your caravan on the flat, and you moved it onto a slope, the 'A' frame mover would quickly loose the ability to control the caravan, and it would start to move down the hill out of control. You would need to reach the brake to stop it, quite a juggling act.
The second major factor over which you have no control, it the condition of the surface on which the hitch drive is operating. As soon as it rains, the coefficient of friction between the wheel and the surface is reduced, add in wet leaves, grass or icy condition, and the situation is made so much worse. Similarly the relatively small diameter of wheel used on these devices does not cope well with gravel or other loose surfaces.
This is where the chassis mounted movers that drive the caravans main wheels score. The same law applies that the draw bar is only equal to the down force on the driven wheels, so you now have the bulk of the caravan on the driven wheel so the drawbar force will be roughly equal to the weight of the caravan. A much more secure situation, and the larger diameter wheels and increased contact area improves performance on loose surfaces.
Caution still has to be used, but there is a much better margin of safety.