When I learned to fly, I was taught using the 'other' technique in Cessna 150s at Cranfield. I was unable to land consistently at a specific point until I was well beyond the first solo stage - touching down somewhere safe on the long runway was seemingly OK.
I also think that I was taught quite poorly.
I didn't really start using point and power consciously until many years later - probably on the Folland Gnat, if I recall correctly.
But having later been 'taught to teach' by the experts at CFS, I cannot understand why anyone would conceivably still wish to teach the 'other' technique.