There is also another issue that may be at play (I don’t have any FDR plots for the mentioned accidents to hand so supposition only) - once pointing at the ground and seeing the IAS winding up the instinctive response is to bring the thrust levers to idle. In an aircraft already out of trim nose down with high pitch up force from the engines, the aggravation of the out of trim condition by removing the thrust could be what rendered the aircraft uncontrollable.
Thread drift coming up. Re above quote. During a Singapore court case concerning the Silk Air B737 MIA 185 crash (deliberate although unproven) FDR evidence indicated the pilot rolled the aircraft inverted and pulled through to the vertical while simultaneously selecting full forward stab trim. The company defence claimed the first officer probably forgot to close the thrust levers or select speed brake while performing an emergency descent due perceived pressurisation failure, while the captain was absent from the cockpit. In other words the first officer stuffed up the emergency descent. At the time, indications were the defence seemed intent on shifting any blame away from the captain for the event.
Asked how come therefore the 737 did a purported emergency descent and went in with high power still applied and no speed brake use, the expert witness for the defence said if you apply high thrust in underslung engines the nose will tend to rise. It could therefore be argued the pilot was using high power to try and raise the nose after completing the emergency descent. The aircraft passed Mach One in the dive and broke up before hitting the ground.