I do not believe it is genetic. My parents have healthy jaws/bites. My oldest brother and me have almost the same jaw and chin shape, as well as teeth shape. But his teeth grew in perfectly straight and he has barely ever had problems with them, and his arches are nicely wide. Same for my sister though she takes up after mother.
I on the other hand completely wrecked my baby teeth growing up because of the amount of sugar and junkfood I consumed, some of them pretty much rotted off. Then when my permanent teeth grew in I didn't improve my habbits so I ended up with very narrow arches full of crowding and a recessed mandible and orbital rims. My other brother also had these bad habbits and his problems were the same plus extraction orthodontics with awful headgear recessed his whole maxilla.
If I have kids, I do not worry about them developing these problems because I'd make sure their diets were healthy.