The parabolic rail really grabs into the face of the wave. They cut back best because the wider tail and the narrower mid-section let the tail flex more. Turning and tracking into the wave is all about flex. I make the concave a little deeper to allow more flex as well as making the convex rolls on the sides of the concave more pronounced. This pulls the rail a little more in the wave and it makes the board want to actually pull up higher into the face.
So, if you are dedicated to standing on the alaia, this is the shape for you!