Why rudder and elevator in a turn?

One needs to balance forces on the tail in two dimensions in order to keep the plane flight path horizontal (or maintain desired climb/decent) while maintaining the desired rate of turn and airspeed -- without excessive "sliding" of the aircraft (nice to have the centrifugal force + gravity vector perpendicular to the wings). Engine power setting is also a factor to fly a precise path (curved or straight) at a precise airspeed.

Moving only the elevator gives balance in only one diagonal (when banked for a turn) dimension. Adding in the rudder gives the second, perpendicular dimension. The balance will be different for different airspeeds and rates of turn -- necessitating differing amounts and ratios of elevator/rudder deflection.

Thus, both the rudder and elevator must be used to differing degrees based on the airspeed, rate of turn, desired rate of climb/decent, desired "slide/slip" (or lack thereof), aerodynamics & balance of the particular aircraft, and physics.

Of course, with training and practice, the pilot's brain and "feel" integrates all this to provide the desired result without "thinking" -- just as in many other complex human physical actions.

At least, I think so Anyhow, just another way to say what has been said above.