It is not about air space it is about structural strength to reduce the rotational affect of the bridge due to the tension of the strings. The rise is actually a dome imparted by the shape of the connecting surface of the fan braces. A dome resist the rotation forces of the bridge better than a flat plate On classical it is typically on the area around the bridge for about 3" or so past the extremes of the bridge. On a steel String it is pretty much the total top and back that is domed. That said. If you build dead flat the strings tension will pull the top in to a dome shape but you will not have the benefit of the added strength of a dome that is braced with the shape dome. Instead you have shape that is forced by the loading forces of the strings. Many great guitars are built as both dome tops and flat tops.
So know the reason. Time to research the science behind it.
