It is only natural for Son Heung-min to be the captain

You are all underestimating Son Heung-min way too much.
He is an all-time legend for the national team.
To give you an idea of his achievements, he has 140 career goals in the EPL.
Park Ji-sung, who was known for being strong in big matches, has fewer than 20 career goals; that is the level of the gap between them.
A player like that absolutely deserves to be the captain.
He exerts influence on the pitch, even over the opposing team.
If a player whose skill level is two or three tiers lower than Messi's—someone described as timid or introverted—were to be the captain, people might say, "Sure, that's possible," but in reality, that's not how it works.
People talk about "leadership" this and that, but winning the EPL Golden Boot title is leadership in itself.
In the professional world, you are recognized through your skills; being easygoing, kind, or a good talker is not what leadership is about.
It makes no sense to bypass Son Heung-min and suggest a K-League captain as the national team captain just because they "act like a leader."
That is why the '96 line should not be the captains either.
One of them has the skill but has said he has no lingering attachment to the national team, right?
One has never even played in a major league,
and one actually doesn't have the skill level to be selected for the national team right now.
If we are looking at the long term, it is only right to entrust it to Lee Kang-in.