Even in a small institutes with only 2 staff and 2 Korean teachers a native English teacher is desired. Since people here learn English in middle school they don't get a chance to practice talking. They know grammar and vocabulary, but are shy and scared to make mistakes when speaking English. The parents want their children to be sent to institutes with native speakers so they will have good pronunciation and do well speaking English. Some mothers even try not speaking Korean to their babies.
Some rich kids are send off to the U.S. to study English.
This was a hot issue a few months ago. For the schools, it's good to have native teachers. They can advertise that they have one and get more students. Today's English education situation Traditionally English learning was not conversationally based. And most teachers were not good at speaking English.