As I see it, there are three advantages to the recurve:
1 They facilitate the draw cut by forcing the target into the edge.
2 They tend to hit a chopping target at a slight angle which concentrates the chopping pressure on a smaller area of the edge, giving deeper penetration.
3 More of the weight of the blade is forward, where a chopping impact would be.
Kukris are recurves, if you look carefully.
They are almost impossible to sharpen properly on a flat stone, but rods work well. It may chop somewhat better than an S6, but a 10" blade is going to be much more effective because of the additional weight and blade speed at the chopping area in the front of the blade.

Edited: There is one more thing: They really look cool.