Clearly both work, but point'n'power (power adjusts speed) tends to give a more stable approach and a more accurate touchdown position. The bottom line is that you have to teach what everyone else in the school teaches or students are going to become confused.
Most SEP instructors seem to teach attitude for speed so I only tend to introduce p'n'p when converting people onto complex types, to twins, or if they ask to do it on a BFR.
(Small error in the OP - the aiming point is held constant in the windscreen until the flare; the power is adjusted to maintain the correct speed - the airspeed is not "constantly varying")
HFD