Kirk beaming down to a planet, spending a few hours there at best, and then changing the entire way their society works is probably half of TOS' planetside episodes.I dunno, it would be a bit strange to have Kirk save they planet and end slavery/racism by the end of the episode...
Off the top of my head, Kirk does this in "Return of the Archons," "Miri," "A Taste of Armageddon," "This Side of Paradise," "Friday's Child," "The Apple," "Mirror, Mirror," "A Private Little War," "The Gamesters of Triskelion," "A Piece of the Action," "Patterns of Force," "The Omega Glory," "For The World Is Hollow...," "The Cloudminders," and probably some others I'm forgetting. Kirk remaking an entire planet's society is one of the basic tropes of the show.
Kirk ending slavery on a planet wouldn't be strange, it'd be Tuesday.