Nobody has mentioned that an engine's power output is
non-linear with respect to RPM...Therefore,A CS propcan alter pitch to allow the engine to stay on the peak of it's power/ torque curve.
If you like, it's the Aero equivalent of a car's CVT automatic gearbox...there really isn't room on the average SEP to put a multi-speed gearbox on the front of the engine...and changing gear might prove a challenge to many pilots