The biggest reason are the Japanese and the South Koreans themselves, not the Americans, or at least as far as how quickly and competently they developed. Part of this was simply leadership: you'd much rather have the LDP or Park Chung Hee than, say, Marcos. (Look at what Kagame is doing in Rwanda, and who he is taking inspiration from-Deng, Park, Lee Kwan Yew. If Africa had more leaders like him and less Mobutus and Dergs in the 60s, they wouldn't be in this mess, given that the ROK was poorer than they were back then-although that's in part the West's fault, to be fair.) And they literally worked their fingers to the bone, in Korea especially: I don't think people quite comprehend just what the Koreans pulled off in a space of three or four decades.

In part because in the 40s and 50s, we were willing to stay and defend them as long as necessary. Weird as it sounds, Americans actually believed in their mission back then, for both good and ill. The USA was so obviously successful in the 50s, especially compared to the Soviet Union, that few in Japan or South Korea needed prompting to look there for examples. There was relatively little of the appeal of 3rd world socialism seen in places like Indonesia or Vietnam, who were under European colonizers, by contrast. Japan obviously was an empire, Marxism lacked the same anti-imperialist appeal. Korea was a Japanese colony, so it did have some appeal there, but in a very different way than what you saw with Sukarno or Ho Chi Minh. Kim-Il Sung based a lot of his rule off of Imperial Japan.

And in part because everything was absolutely destroyed-Korea was far more of a post-WWII than a pre-Vietnam conflict in terms of conventional fighting with tanks and bombers, with the corresponding scope of the destruction, physically and psychologically-which perversely made rebuilding from scratch easier.