I think the desire for stronger female characters in media is what drives the push for Kairi. It's too bad it's misplaced with her. The Kairi character has never been worthy of that energy. Even when she was at her "best" (KH1), she was only an object. Sora and Riku were already great characters in that first game... Even Ansem SOD, who was a bit bland (like most of KH's final villains), had Billy Zane's great performance lifting it. They didn't need follow-up games to make them that way. It would only be to this game's detriment to make the least interesting character in the series a playable character you're stuck with for 10+ hours. Well, I'd say that for the series as a whole, too, really.
Besides, three scenarios were already proven to be a mistake in BbS, imo. I would never have wanted a repeat of that, least of all for that character. And to the point about a game being written with her story in mind, that is how it should happen for Kairi if it ever happens for her. (Not that I want it, but speaking hypothetically.) But that kind of contradicts your point in regards to this game though? So much of 3D revolves around Sora nearly becoming a vessel, Riku being a Dream Eater... Sort of a continuation of CoM and 2 where Riku operates as a shadow to Sora in many ways, willing to do what Sora can't or wouldn't. Where would Kairi have fit in all of that? Other than to completely alter the story to suit her, or divvy up a part of Riku's role and give it to her. No thanks. And it would be sort of laughable for Kairi to become a Keyblade Master, and not Sora.... I remember there being a lot of eyerolls about Riku getting that before Sora, it would've been even worse if it happened with a character who hadn't done anything for the entire series prior.