Let's say you have a properly trimmed airplane that for some reason gets into a nose-high attitude and begins to fall as AF447 did. Is there a regime in which you just cannot get out of it? Will the nose always come down if you have proper trim and take the thrust down to idle if necessary? Is there a danger of entering a flat spin? How to avoid that?
I keep thinking some sort of emergency reaction control to push the nose down might work. Some small solid rockets just for emergency use.