Yeah, we get told that. In fact, however, the nose will drop all by itself in
most light aircraft. If the pilot doesn't stop it from doing so.

Your point is well taken. No question about that. From ASF's
material, a pilot will take 4 to 10 seonds to "realize" or "register"
the trouble. So there isn't really much time left. Plus the
instructor usually will take over when he "feels" the student can't
handle it. But in a less-forgiving aircraft, the instructor must be
very fast and determined, otherwise, it can cause death like this.