Tsunade is exactly the kind of person who would keep such a tool around. Because she's lazy yet has lots of pride and also intelligence (at least sometimes). A capable person like Shizune removes some of her most boring work but at the same time takes care that Tsunade doesn't slip too far. As we have seen, Tsunade doesn't really keep Shizune in fear but actually tries to keep her bad habits in check when Shizune is around and work really would need to get done.