Think about it this way:
If she gets the chance to be a protagonist of an installment, what would her arc be about? What are her demons, her desires, what would her journey teach her, etc.
I can't think of anything that troubles her except Sora's well being.
Her entire character revolves around Sora. If she goes on this adventure, it'll be about Sora and getting him back. The DLC, while having her be able to cement her place as a a decent fighter at best, still doesn't get to the core problem. They almost had something when she spoke about Naminé's existence in KH3, but that didn't amount to anything. She didn't even get to interact with her Nobody. Majority of RE: Mind was about her romance with Sora. Let's be real.
Speaking of Naminé, I'll use her as an example in terms of what there is to work with. She's the best female character in terms of personality change, development, and growth. And like Riku's, it expanded throughout multiple games. Without the amount screen time and effort he received, but this is Nomura handling females.
CoM:
Born alone and remaining friendless, with no place to belong (until KH3, I think), she desired company. She could shift through all these happy memories of Sora with his friends, so it stands to reason that craving that, she inadvertently summons Sora. Which she admitted to -
"I was alone for so long. I couldn't bear it anymore...so I beckoned your heart to lead you here."
And of course, Marluxia and Larxene took great advantage of that.
So we have this fragile little doormat of a girl, who, aside from some nasty looks given to Larxene, isn't doing much to stand up for herself. She wants to stop this, yet can't figure out how, as she's not a fighter and she's weaponless. It isn't until Axel gives her the opportunity after all that she proceeds to put an end to it. Because of Sora forgiving her for her deceit, she refused to do anything anymore and finally stood up for herself. And got a mean bitchslap from Larxene for it, yes. Still, this is the beginning where she takes charge and gains a semblance of inner strength. The glow up continues onwards from here (i.e. KH2).
Even after all is said and done, we still see her desire and selfishness show, what with her rather bitter remark when Sora chooses his old memories rather than his new ones. She promised she'll fix him (and promised Riku as well that she would).
Days and KH2:
Unfortunately for her, things got complicated, and she was forced to remain neutral with other parts of Sora, despite that she felt for them and didn't want it to occur this way. She did her best in assisting them, to Roxas most especially, whose friends hadn't respected his agency and denied his wishes to know what's going on. Naminé fulfilled that and took in his individuality and how he deserves to be aware of things and make his own decisions. They related to one another for their similar fates and bonded through that.
All this time, she's been verbally abused by Diz about how disposable she is, how she should be nothing, so her mentality steers that direction too, and her entire year of life has basically been stuck inside four walls watching others enjoy, well, childhood. That's why she draws the memories of others (or so Diz thinks in his Secret Reports).
Nonetheless, she's gotten better. She's way more confident, rebellious, and despite not having a weapon, is active in the prologue, helping Roxas by hacking Diz's computer and approaching Roxas with such HBIC energy that I was floored. Left him all bashful while he rubbed the back of his head...then she turns and walks off. I remember guffawing. And it doesn't end there. She squares up to Saïx with Kairi, busts Kairi out of jail, and summons a portal of Darkness to get them out of The World That Never Was.
Coded:
We can see her guilt about those she hurt. It isn't really her fault, she was forced to, but considering how she summoned Sora over in the first place, she more than likely feels partly responsible. It's her that informs the rest of those who need saving.
Then we get to KH3 where we see the accumulation of her side arc via her thought process. She still has a sense of will, what with calling Lingering Will to legit save everyone's asses. But based on the conversation with Sora, she still has low self esteem. Or feels unneeded or unwanted. Remember, she's been friendless and abused her entire life. That's surprisingly realistic.
So we have plot threads for her:
• See her learn and understand that she's cared about through her relationships if she does really live in Twilight Town and gain some damn self esteem, geezus.
• Come to terms with her guilt, and this includes Repliku's ultimate choice.
• She doesn't have a weapon, so you have a whole game where she's able to grow and train with one if they allow her to.
• Sora still hasn't thanked her for some goddamn reason.
• She's powerful with her memory ability, she can dig so deep now that she's able to guide a spirit of Terra through his connection to Ventus who is connected to Sora. And with dreams and other themes being explored currently, that's her MO.
In fact, she's probably the one studying Roxas' and Xion's memories (they are "Sora"), but she can do much more than that. She can trace connections of the Heart. Nomura has a goldmine of a walking, talking Deus Ex machina here (next to Kairi).
But I digress.
With Naminé, you can do stuff with her. With Kairi, I struggle with what she can acquire in her own game. As in, that has nothing to Sora. How it would be about her.
TL;DR:
Until Kairi disassociates from Sora and stops merely being a love interest whose world revolves around him, the main issue will persist and not change.
If there is a Kairi based game, I can only hope they do well by her, because if they fail, those who still hold hope for her potential might throw the towel.
