Kat believes that Hana will effectively replace August, and regardless of what happens in the next few weeks/months, change will come. I can't figure out Kat's ultimate goal, whether to fully unfetter herself with the new management, or transforming the club into her ultimate utopian vision and then retiring, having established her legacy. Oh she'll no doubt return as an exhibition spectator if she does retire.
She does seem to be wanting Hana to replace her, but again, I don't know if that's the goal, especially since she seems more committed to making Edwin her heir. If Kat is planning to stay for a long time, then Kat's logical strategy, knowing Hana's initial attitude toward the club, would be to make Hana invested not just financially, but in heart and mind. If Hana has had personal "investment" in the amenities, and thus has personal guilt/responsibility, not just associative, then she will be disarmed in viewing "those evil people who need to be taken down," when she is now one of those "evil people" by both shareholder, and participant, making it a lot harder for Hana to go through with "burning the house down". I obviously don't know TD's intentions, nor the depth of Kat's master planning, but it does seem like one of Kat's strategies in transforming Hana is giving her a sob story to root for, thus showing/convincing her that the Club is indeed helpful to women, not solely degrading. Thus she gets Rose, who strikes at Hana's sympathetic heartstrings, and Edwin, counting on him favoring Rose due to his background, which leads him to helping her specifically, thus Kat decides before Rose and Edwin are at the Club that Rose will win the competition.
Naturally the problem is this might take away too much player agency, so I don’t know if TD has planned this. The counter-argument could be made that the player agency comes in with Edwin choosing whether or not to help Rose, thus rejecting her muddles Kat's plans, forcing her to adjust. It can also be suggested that Kat also choose Felicia, being a sex-fanatic peer to Hana competing for a good time, and Veronica, the image of a strong independent woman crossing the finish line standing tall and "undegraded" thus challenging Hana's paradigm. Yes, Veronica had to qualify, but that was so clearly one-sided in focusing on endurance tests, so Lucy never had a shot.