Korea has not closed the borders. Korea has effectively controlled the issue without controlling the borders. In fact in the past week, 30% of new cases are Korean citizens returning to Korea across the boarders.
If anything, boarders should only be closed to tourists and non-essential business,. Anyone travelling during these times is an idiot or desparate. We shouldn't punish the desparate. Testing and social distancing work. Closing the boarders just means people will lose trust in government and start hiding.