Gisaeng were designated as 'slave/lower caste'. Many were trained in art, music, literature and medicine. They were 'owned' by the provincial governments. The well educated ones served in the royal palace and entertained noble men. Gisaeng were not technically prostitutes either at the beginning. Gisaeng do not exist in modern Korean Society.
Geisha were/are entertainers, well versed in art and music and conversation. While some had sex with their male guests, primary role was entertainment. Geisha are still present in modern Japanese society.
I think the major reason is once you're forced in....there's no coming out. Unless a Gisaeng was bought by a patron or sponsor, she would remain a Gisaeng until she died. All her female children will become Gisaeng. And their children and their children's children.......
(I like sweetandtasty coz she gives good insight on korean food and culture and sayings. If you're interested in taking your love of things korean to the next level, she might be a good place to start.)