Hey Kemosabi,
Windsurfing sails have loads of downhaul force applied. I normally use a 6:1 pulley, and pull probably around 20 kg on the end, so that's 120 kg of force on the sail.
With no boom on the sail, the mast is bent to the right shape, and all the tension is down the "Area of greatest tension" line as you described in your drawing.
Think of it not like an archer pulling back on the bow, but the bow at rest with lots of tension in the drawstring.
As for the battens, once you tension the downhaul, these will start to do what you expect, ie produce an airfoil shape in the sail. They will only be flat if you don't have enough downhaul.
Of course, this all changes when you recut it into a landyacht sail, but it's good to get an idea of how it was originally designed before modifying it