Bernoullii's principle states that when you slow an air mass, it increases in pressure, when the speed of an airmass increases, the pressure drops.
It is only a principle or a statement of physical activity, wrongly applied to why lift is generated. The principle DOES happen on an airfoil, but it is the laws of physics (Newton) that actually make it fly.
I would gesture that the only reason you have a wing in the typical airfoil shape instead of flat, is to more closley follow the natural flow of the airmass as to allow a clean laminar flow