If one holds with the premise that Attitude controls airspeed and power controls rate of descent, then to take off, one should lower the nose to accelerate down the runway and at an appropriate speed apply power to commence climbing.
As this procedure is unlikely to result in a satisfactory take off, one can assume that it is safe to say that power primarily controls airspeed, and (pitch) attitude primarily controls aim point. Both have an affect on the other, so it is not uncommon to have to adjust both to achieve the desired flight path and airspeed.
To teach in GA the opposite, whist it can be argured to be true, is simply trying to complicate what should be straight forward, IMHO.