Comment by kqr

Don't get me wrong -- for practical flight it is really important to expand the reasonable range of angles of attack because angle of attack is one of very few ways one has of controlling the aircraft.

But for explaining how lift appears, it is an irrelevant detail.

The purpose of modeling is not to mimick reality at high fidelity but to focus attention on the o parameters that matter for a specific situation. When you change the situation (going from explaining how lift happens to trying to fly) it is not surprising to have to switch to a different model.