Earlier quoted context omitted.
"Longer path" has no bearing on reality. A flat plate can generate plenty of lift even with both sides the same. It's also hard to define "path," as the air starts convecting well ahead of the wing in subsonic flow.
Sorry, but I don't subscribe to the 'flat plate' theory. There is a reason that almost every commercial (and most military) aircraft have leading edge slats to generate lift at lower speeds (by making the top of the wing more convex and the bottom of the wing more concave). If pure 'flat plate' theory was valid, then all those aircraft speeding down the runway with the leading edge of their wings canted downwards 20…
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.