I would like to tell you some of the theoric characteristhics of profiles:
1-Concave profile: This is the common one of sails, the single skin profile. Is the one which gets the biggest force for a given intesity of wind. But it is also the one which has the worst Lift/Drag ratio.
2-Symetric profile: The one of fins. (It's most used property is that it can work in both sides, but we are now not speaking about this). Is the one which produces the less force for a given wind, but best L/D ratio.
3-Flat-Convex profile: Flat in one side, cambered in the oher. It has medium characteristhics between 1 and 2, of course.
4-You can also find profiles which are concave-concave, but doubble skin, or convex-convex, but not symetrics. You would get intermedium propertis with them.´
For high speed vehicles flying at 800km/h (turbine airplanes), you use asymetric convex-convex profile. For medium speed vehicles flying at 100-200km/h (sportive airplanes), you use flat-convex profiles. For very low speed vehicles, sailing at 20-70km/h (windsurfing boards), you use concave shapes to produce enough power in small sail. Otherwhise you would need bigger sail to compensate the lost in power.
We can consider then that a wide luff sail is an intermediate concept between concave sail and flat-convex. Acording to all i said, now you understand why this design is only used in huge sails. And like this you can get better upwind angles.
A thing I would like to add is that if you want to take more power from a given size of sail, what you can do is to divide it in two sails. So that you have a rig looking like the rig of a boat. Consisting in two sails. Like this you would get more power but worst L/D ratio. Good idea for downwinds. What about putting a zip from up to down in the sail to open it in downwinds and close it in upwinds?
Here i put the link of an interseting web page where you can see wing sails.