I was taught that immediately after power loss, gain as much height as possible with the energy that`s available prior to the glide.
Well see how much height you gain from average GA single bumbling along at 100 kts if engine completely and suddenly quits! Hardly worth the
That is the problem with instructor generalisations; in this case engine failure and immediate actions.
If I recall from my Air Force training several decades back, the immediate pull up to gain height following engine failure, was meant to apply for low flying sequences. By low flying, I meant 200 feet which in those days was military low flying.
Obviously in a light single like a C172, by the time you have recovered from the shock of a sudden engine failure, 20 knots is lost in a flash so a pull up brings its own dangers and that is an immediate bunt again to fine-tune best glide speed.
So much depends on the IAS at time of engine failure. Where you can zoom rapidly another 200 feet if flying already at 200 ft, it gives breathing space if only for a few seconds. But again, so much depends on the skill of the pilot.
But as far as a pre-flight briefing is concerned, before undergoing a dual low flying sequence, it is up to the instructor to explain all the factors affecting any decision to trade speed for height. That includes airspeed at time of engine failure