Canspam
As has been pointed out, both the stick and the throttle have an impact on both speed and flightpath, and after a while it will all become second nature. But that's no help when you're starting to learn, so most FIs assign an individual function to each control.
Because of the glide and full power climb scenarios already described, where attitude clearly controls speed, many FIs don't want to teach a different method for the final approach; it's all too confusing. However, I feel strongly that FOR MOST STUDENTS that the 'point and shoot' technique is more intuitive and easier to grasp.
I don't do a huge amount of ab-initio teaching, mostly postPPL training, but my experience has definitely been that power for speed on final approach works best. I was lucky enough to spend a couple of days with John Farley a few months ago, who in his articles always highlights the situation where a pilot gets low and slow on final approach; the only option there is power for speed! He also claims that most air forces and flying organisations around the world use this approach, apart from the US Navy - and GA....