Umm no, at zero degrees AoA as the first diagram on the page shows, a flat plate does not generate lift. But nobody actually questions that a flat shape can generate lift; we all made paper planes as a kid.

But every airfoil has an equilibrium angle of attack (not always stable with velocity) where it generates zero lift. The chordal angle of attack is for convenience because it depends only on airfoil geometry and not ambient velocity, but it isn't a fundamental physical property of the airfoil.

If we treat the angle where zero lift is generated as the base angle for an airfoil, then all airfoils generate lift depending on their angle relative to that, including a flat plane. As the GP says, other properties are the dominant factor in airfoil geometry.

When introducing airfoils I think it is more useful to start from a plane than a traditional airfoil shape; the math and intuitions are much clearer from there.

Paper airplanes do not have barndoor wings, though. Most of them have stepped camber through the way they are folded.

It's not finished but I started writing this to clarify: https://entropicthoughts.com/paper-airplane-aerodynamic-stab...

Scroll down to "trim and angle of attack".

(I hope there's nothing embarrassing in there. It's an old, early draft.)

Uncambered airfoils also don't generate lift at zero degrees. What constitutes "0" for curved airfoils is convenience. You want lift, you put a flat plate on an angle, anything fancier is for Lift/Drag, Thrust/Weight, etc.

There are about a million places incorrectly "explaining" that airfoils create lift because the top path is longer and this means the air has to go faster. A flat plate would not create lift in that case. The fact that paper airplanes obviously can fly somehow never stops people from repeating this.