Pointing the nose down when you are falling at 123mph requires a certain amount of confidence and the certainty that that is the right thing to do.
More likely you'd stick to standard procedures.
Perhaps all pilots should start in gliders. When you start falling, you damn well know it. There's few instruments and few controls, so it's stick forward, keep the wings level and you just _know_ from your ass and the noise when you have lift and steering available again.
With AF447, what seems wrong to me is, as I read it, the automatics quit when they reached their limits of trim and control, and quit leaving all the control surfaces at their program-permitted-extreems. It just handed the ship back to the pilots with all control surfaces in maximum and unknown & unexpected configuration.
The automatics should have been programmed to return all controls to neutral, trims to zero etc, before quitting. At least leave the pilots with an average aero-dynamic brick, rather than a brick with random control surfaces.