A bit late to reply, but I had to think of your post while spending some hours idly staring at at the top of an airliner wing today. Slats (and non-flat airfoils in general, I suspect) are there to allow a harder angle of attack ("amount of pointing up relative to the direction of movement") without stalling.

You can push the air hard on the underside, but on the top side, you have to gently accelerate the flow downwards, or else it forms vortices and you suddenly lose a significant fraction of the amount of air you would otherwise deflect downwards.