So again why apply full power have the aircraft start to accelerate and then have the aircraft rotate to the climb attitude and then start slowing down ? It makes a lot more sense to establish the attitude first and then smoothly apply full power. It also is easier for the student to keep the aircraft balanced ( ie prevent yaw) if the aircraft is already in the climbing attitude.
If you apply the power, secondary effect pitches it up anyway so saving effort and giving a faster and more efficient transition to the climb, there is no noticeable acceleration either, and I do not see why balance is any easier applying power after establishing climb attitude. certainly the way I was taught.