- no way Jose! Unless you have been indulging in some aeros or a major upset, a reduction of a few degrees is sufficient to silence the stick shaker or at worst to unstall the wing - to pitch 10-20 down from a normal high level stall AoA of around 5-7 degrees would be horrendous and would upset me as well as Tyro, spilling our 'retired' G&Ts in First and would undoubtably "result in a number of thousand feet loss of altitude" if not bits falling off the a/c.
That must be pitch and even then that is a lot--5-10 degrees nose down would be like it. Due to being power-limited, the only means to increase EAS and Mach is gravity.
The information from the AF447 FDR now shows that the aircraft was descending for three minutes with and Angle of Attack of 40º or so - so it should be obvious to see now that, in this type of upset at high altitude resulting in a deep stall, even 10-20º reduction in pitch (OR AoA) may not be enough.
On the GLF we teach to keep pitch attitude, and just add FULL MAX WAR POWER, and the aircraft will power itself out of the stall.
...which is exactly what the AF crew did - maintained the normal after take-off climb pitch (about 15º nose up) with full power for three minutes - and remained stalled until the event ended.
I think you ( and many others) would be rather appalled at what is required by YSBK CASA office FOI's, in recent times, highly experienced pilots have been failed on base checks for ANY decrease in attitude during stall and recovery. "Powering" out of the stall with zero loss of height has been "informally" adopted as the "standard".
Then they are teaching people to die. Stall recovery is exactly that - un-stall the wing, and
everything else is secondary (including terrain clearance). Minimising height loss with a stall recovery at altitude is simply not a consideration - if the pilot is so out of the loop that the aircraft has stalled in the first place, then the recovery is going to take some height.