Now, I shouldn't say that every car in the 1920s was like the Dodge in this clip. There were a handful of sports cars and race cars back then that weren't very SUV-like, for instance. The standard family car, whether it was a Dodge or a Model T or a Chevrolet or whatever, did have the features of a modern SUV. They came with wagon-like bodies and considerable ground clearance, and (apparently) you roll them right back over if they flipped.
It's easy to see why - look at the conditions of what passes for a road and you'd want your family sedan to work like truck, too.
(Hat tip to desertdog5051!)