A stall during an EFATO when properly trimmed has to be induced by the pilot pulling back, allowing speed to bleed off. From my limited experience flying C172/PA-28, the amount of pulling back to cause such a stall has to be fairly significant and not easily missed. Is it easier to miss this sign than I realise, or does panic simply cause pilots to miss this important warning sign?
If the aeroplane is climbing after take off at full power, it will be trimmed for that - no pulling back required.
When the engine fails the aeroplane, unless the pilot does something about it, will remain pitched nose high (not quite as high as before as removal of power will induce pitch reduction in itself), the speed will rapidly bleed off due the nose-up pitch and no power, and within a few seconds (3 in this case of a benign PA38) the stalling angle will be exceeded and the aeroplane will depart controlled flight. All this with no pulling back.
In very light aeroplanes flown to max climb performance the stall will occur pretty much as soon as the engine fails. At Barton about 30 years ago a highly experienced GA instructor, examiner, and B737 training captain (the guy who had meticulously checked me out on the Chipmunk) was climbing at max rate in an Issacs Fury. The engine failed and the Fury stalled and spun immediately. He was seriously injured.
When the engine fails in a climb it is essential to LOWER THE NOSE IMMEDIATELY, and perhaps quite violently, to prevent loss of control.