For years I thought the idea of applying power at the same time as lowering the nose during stall recovery was to give immediate increase in slipstream over the various lifting surface and thus give more lift - thereby recovering from the stall. Prop aircraft only, of course. Have I got it wrong over all these years?
One way or another the aim is to recover from a stall. Lower the angle of attack (stick forward) and power simultaneously does just that. Jets are different. Increase thrust while simultaneously lowering the nose a few degrees to the horizon or just below, should increases speed hopefully and thus recovery from a stall should occur.
High altitude stall recovery is a bit different. You need to count on losing 3-4000 feet while deliberately picking up to a safe manoeuvering speed. Important to keep the aircraft accelerating downhill in this case to avoid secondary stall symptoms caused by nose wanting to rise with increasing IAS.
The Boeing 737 FCTM gives a good hint on defining "safe speed" before level flight is started. Vref 40 plus 100 knots. Typically around 210-230 knots IAS before levelling out or even attain severe turbulence speed before attempting to level out if the cause of the problem in the first place was severe turbulence penetration followed by an upset in IMC