You will be surprised at how vigorously the nose must be lowered if the engine fails at climb-out speed in, say, a PA38. Not lowering it will kill you, as a guy I knew discovered at Barton a few years back. He did get out a mayday though, when instead he should have flown the bleedin' aeroplane!
If you have never had an EFATO you may wonder how you will react if it happens. Will you freeze or will you get the nose down? I found instinct and training took over - there was no thinking involved; as the power dissipated, forward went the stick (aeros experience might be a help here as energy management in a low powered type like the Chipmunk is ingrained!).
I know we practice for it a lot (at least we should!) but having the power go when you're not expecting it isn't quite the same. That's why we should expect it - on every take off. Be surprised if it keeps running!