Why did it take so long for helicopters to be developed/in use?
The useful payload and the robustness of rotorcraft were not sufficient for the rough conditions on the front. Only when turbines were available with their much better power-to-weight ratio and high reliability did helicopters offer a real advantage to the military.

The de Cierva autogyro line was begun in 1920, but de Cierva focused on building unstallable GA aircraft, not weapons. The same can be said for Henrich Focke, who improved on de Cierva's designs (which he built under license) with the Fa-61, which is considered the first practical helicopter.

The only helicopters to be used by the military were the designs of Anton Flettner who used two intermeshing rotors with considerable success, the transport helicopter Fa-223 with two rotors on outriggers and the Sikorsky R-4. The Flettner 282 and the Fa-223 were ordered by the Luftwaffe, but development took a long time, with many new problems to be overcome. In the end, they came too late to be used in any quantity.

The Sikorsky design was unstable and needed considerable pilot attention. Just watch how poor Igor is working the stick to keep the VS-300 straight! It also needed years of refinement before it could be used by the military. This was the R-4 which saw limited use for rescue missions from 1944 on.

Just because something can be demonstrated once does not imply it is ready for widespread use.