You avoid "chunky" soles that have lugs. If you fall, the lugs will keep the foot from sliding out of the stirrups. The stirrups hang up on the rough bottoms. This increases your chances of being dragged. Find some sort of slick bottom shoe.
See how there is a heel, a smooth portion and then there are bars going across? If your foot goes forward in the stirrup or iron and you fall off, the stirrup/iron is going to get stuck on those bars and you'll get dragged.
The heel of the boot is to keep your entire foot from going through the stirrup/iron. Those bars across the front are going to keep your foot from falling out when you fall.
Good point about the treads on those partiular boots. Now that I think about it, I haven't seen any riding boot, that includes all the Ariat and Mountain Horse Endurance/Terrain boots -that have treads like that.