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the united states pushed radio (and then slightly later television) heavily when they were helping rebuild south korea in the post-fighting period.
there was a military owned radio station called afn korea that played a lot of american pop/swing/jazz during the rebuild
music became a very important part of the culture and eventually yes, the government did help fund some hallyu ventures in the early 2000s although they weren't very successful and youtube ended up being the most relevant thing to help push it
t. took a class that spent 2 weeks on this