There is really no advantage to carrying USD in Korea. Most local banks will exchange USD to Korean Won. All banks except Standard Chartered and Post Office open from 9 AM to 4 PM, Monday ~ Friday. Standard Chartered and Post Office open until 4:30 PM. No banks open on weekends, except the airport locations.
Credit cards are widely used in Korea including taxis. Not all ATMs in Korea can accept foreign credit cards, but global ATMs can be found at limited locations. Citibank Korea has globalized all of its ATMs in Korea.