Your spot on Frank,
My take on it is in the 2 seconds of WTF is happening was enough to dissipate the airspeed and as per human nature pull back on the stick cause the grounds coming up at me
Hard to do to push it over when the grounds coming at you
I think a thorough brief on EFATO could save the day as it is fresh in your mind prior to take off
Engine fails push forward and maintain airspeed
I say it out loud every time I take off as do I full power is attained, airspeed is alive & T’s & P’s are ok
Sad fact is until it happens you never really know how you will react, the WTF moment can catch you out
Alf