Under normal circumstances, the car does not turn until commanded to do so; ditto the airplane. The driver and the pilot use their controls (definition of control: "the power to influence or direct ... the course of events") to manipulate forces for the desired result. Without these controls, the operator cannot manipulate the forces/direct the outcomes. Not sure why some see a disconnect between the controls and the forces over which they exert influence.
Once the bank angle has been set in the airplane, the type, shape, and quality of the resulting turn (and there are many turns the pilot may be able to choose from) is primarily (sorry you don't like that word) determined by elevator actions.
Of course we use all three controls, and here's exactly what they do:
- Aileron controls roll/bank (head-to-hip movement of the nose and wingtips relative to the pilot, regardless of the attitude)
- Rudder controls yaw (ear-to-ear movement of the nose and wingtips)
- Elevator controls pitch = AoA = G-load = lines and arcs (head-to-foot movement of the nose and wingtips).
There are secondary effects associated with each control, too: rolling comes with adverse yaw, pitching can have gyroscopic effects in roll and yaw, yawing comes with secondary rolling and possibly gyroscopic effects in pitch. But let's ignore those for the sake of simplicity here.
If I want or need to bank, I use ailerons. If I want the banking to occur in coordinated flight, I also use the rudder. If I want to manage the curving flightpath, I use the elevator.
Coordinated level turn, smooth air, properly rigged airplane, clockwise turning prop (pilot's POV):
Cruise Config: Roll to 30 degrees of bank with coordinated aileron and rudder. Once achieved, aileron and rudder are neutralized and will stay there until time to roll out. Elevator -- need to pull +1.15 G on the elevator for the desired curve.
Same thing, but now 60 degrees of bank, need to pull +2.0 G on the elevator for the desired curve.
Left Climbing Turn after take off, smooth air, properly rigged airplane, clockwise turning prop (pilot's POV): Coordinated roll to 30 degrees of bank. Once achieved, ailerons neutral, net right rudder needed to cancel the remaining slow flight engine effects. Elevator manages the climbing arc. Too much pull changes the arc and can lead to an accelerated stall while turning.
Commercial Chandelle to the left: Coordinated roll to 30 degrees of bank (no turn). Neutralize. Pull on the elevator sufficiently to arc the airplane upward and leftward to a ground ref 90-degrees from the original heading. Now need opposite aileron to prevent overbanking while aft elevator pulls the airplane through the climbing turn. Rudder as required for coordinated flight (note: as the airplane slows, adverse yaw from the continuous right roll is additive to the engine effects). From the 90 to 180 point, sufficient aft elevator is applied continuously to maintain the nose-up pitch attitude attained at the 90-degree mark. Continuous right aileron is applied to slowly roll from 30 degrees of bank to wings level at the 180 degree mark. Rudder is applied to maintain coordinated flight (note: engine effects continue to increase as speed decays in the last 90 degrees of heading change, adverse yaw from the right roll is still additive). Note this is a left climbing turn with right aileron/right roll applied throughout the climb. Ailerons managing the bank angle, rudder managing the yaw, elevator managing the climbing arc.