With the technical expertise of captured Nazi scientists at the end of WW2, why was there no use of either the V-1 or V-2 technologies in the test bed of Korea? The technology was there, and several years have passed to allow for refinement. So why was there no use of these technologies after WW2?
In the years after World War II, American defense spending plummeted. The limited research and development money available went to nuclear weapons and their delivery vehicles (large aircraft, given the size of nuclear weapons at the time). Guided missiles received comparatively limited funding from the military. The first U.S. cruise missile, the Matador, was built by the Martin Company, which had previously copied the German V-1. That missile began development immediately after the war, but it didn't enter service until 1953 and wasn't deployed until 1954, when it ended up in Germany.
The U.S. military did use one crude guided weapon in the Korean War. In August 1952, Guided Missile Unit 90 of the U.S. Navy launched an attack from the aircraft carrier USS Boxer. Instead of rockets, GMU-90 "flew" six radio-controlled F6F aircraft filled with explosives. These drones were controlled from two "mother" aircraft using a crude television guidance system.
Their target was a bridge at Hungnam (according to Edward Marolda's The United States Navy in the Korean War), and the results were mixed. One hit, one aborted, and four missed.
The drone aircraft program was well-established during World War II, and like so many of the weapons used in Korea, it was largely a WWII program revived for a new conflict. With little funding during the five-year interwar period, there was simply no ability to develop much new.