I think that it was primarily to save weight and reduce drag.
You see corrugated aluminum controls on Ford Trimotors, Junkers, Cessnas from the 1940s on, and even the WACO UPF-7 (an example of the reverse: fabric covered wings, metal ailerons), but these are all relatively slow aircraft.
Smooth fabric is more aerodynamic than corrugated aluminum with universal head rivets sticking out and the steel frame has better strength to weight. I think better construction techniques and more power finally allowed the designers to switch to metal control surfaces.