Your experiences as related concur with mine. Until I did CPL level training the engine failure on take off was not mentioned. When it was taught it came as a welcome surprise.
Interestingly enough, Nr F, your instructor was the first person to teach it to me. This after about 250 hours on type.
These days I sit in the hover and do the usual checks before departure, but the one I add now is the mental rehersal of what to do in the next 30 seconds with an engine failure. Heck I've been doing that before take off for thirty years with a plank wing, why has it taken so long for me to realise that it is vital in a heli too?