It is that simple. That is why I left VNAV climb out because obviously with a climb power setting only pitch could control airspeed. Alt hold or established on a glide slope the autothrottle only controls speed and the pitch axis of the autopilot only controls flight path. Most pilots flew this way before their first automated aircraft. Thrust vs drag = speed. Lift vs gravity = flight path. Any correction with either will eventually require an adjustment in the other axis to balance the other vector. When I was instructing I always showed my students how changing thrust could either increase speed or vertical rate depending on what you did with the elevator. The primary change with thrust is in the horizontal plane with speed. The primary change with the elevator is in the vertical plane with lift.