They are flat on the outside, which is great if you wear a custom orthotic. If you place a custom orthotic into a flat shoe like a chuck, you get a direct transfer of force. There have been many studies on this WRT to cyclist. Cyclist who wore orthotics that brought their foot flat with the shoe/pedal had a direct transfer of energy into the pedal. Those that did not have this support had to first transfer energy in the foot, the foot flattens/caves against the pressure, and then transfers the energy into the pedal.
Now that's just cycling. Let's crank this up a notch to an 800 pound squat. Instead of the weight compressing everything, you end up very stable with evenly distributed force. With stable feet comes stable knees, hips, shoulders...and the importance increases progressively as you travel up the spine.
The other reason is the wide band around the outside. It makes it very easy to "spread the floor" when squatting. They are also very wide soled. Many shoes I've seen, the shoe hangs over the sole. With a chuck, the sole comes up and around the sides, completely covering the shoe. This prevents rolling (as stated above).