Intersections tend to be the most common places for collisions. Unless you do all your riding going around the same block then you'll have to cross just as many intersections when sidewalk riding as doing your riding in the street - and you'll be entering those intersections in a less predictable and visible manner. In addition, you'll be crossing many driveways where exiting/entering traffic isn't expecting anyone to be going over a jogging speed on the sidewalk.

I think it's very likely that in at least a few of the scenes you've covered where a car hit a cyclist who was 'in the road' it was a cyclist who had been on the sidewalk and was in the process of crossing the road or had been pushed out onto the road by a car exiting a driveway.