Hi Schubert - as Frogman said, the progress the Asian countries in general have made with Western music is very impressive over the past few decades - it is not specific to Korea in particular (though my Korean sister-in-law would say they are the best, LOL!). I think the same sort of discipline/work ethic that happens in their schools academically happens in their music teaching now.
Another thing that their governments often do, especially in China and Hong Kong, is send students over here to study, paying for everything, with the understanding that the student is to return to that country and share the knowledge gained. When I was in grad school in San Francisco at the Conservatory, there were many such students there, from all the Far East countries - many pianists, quite a few string players, and a trombone player. All are now back in their home countries teaching others what they learned here, and sending students over here to do what they did.
Another thing that their governments often do, especially in China and Hong Kong, is send students over here to study, paying for everything, with the understanding that the student is to return to that country and share the knowledge gained. When I was in grad school in San Francisco at the Conservatory, there were many such students there, from all the Far East countries - many pianists, quite a few string players, and a trombone player. All are now back in their home countries teaching others what they learned here, and sending students over here to do what they did.