Korean vs foreign coach
I am fundamentally in favor of a local coach, however, in the current KFA structure, there is too much focus on personal benefit and pride instead of Korean football itself.
Most coaches and staff are really old and old school Korean (old boys club). They just want to enrich themselves and want to talk down on everyone. But in modern football and compared to European top tier coaches, those Korean coaches are severely lacking, so first of all there needs to be an admission of their own weaknesses and a growth mindset. They need to be willing to learn and develop but that's difficult when you're 60+ years old and are regarded as a Korean football expert even though you only had modest success decades ago.
So I think on a short term basis, there needs to be a foreign coach who has all the knowledge and experience that Korea needs, even when it is not top tier experience. It needs to be a European football nerd kind of coach who was ignored in Europe but shows some genuine interest in Korea. It can't be one of the crazy dudes who go nuts once you give them a bit of responsibility, so a nerdy dude with reasonable temper and sense of responsibility. We should put a bunch of younger local coaches (maybe in their forties) under that person to learn with a view on nurturing them to become NT coaches long term.
Then, while we fix the KFA issues, in a few years we should have a setup to develop a Korean footballing identity and the right tools to do so and then we need to trust one of those younger local coaches and support them long term.