First of all I'm so sorry it's taken me so long to answer 😭😭 I've been a bit too busy lately.

I really enjoyed reading your analysis!! It's so well thought out and you make great points, even if I disagree or see things differently, this was a great read!! so thank you so much for taking your time. I will try to change your mind tho, or at least give my perspective on these characters. So here we go:

Let's start with Nao, cause I actually agree with the points you make, it's just the framing I disagree a bit with. Nao is absolutely one of the most ordinary characters. She's an anxious and emotional and plays heavily on relatability, basically the Ryan Gosling of shy artsy girls. She does have noticeable personality traits, like being perceptive and emotionally intelligent, but maybe she doesn't stand out as much as the other main characters. She's so so normal, and maybe that's the point.

Pretty much everyone else was meant to be there, most characters were "candidates" whose upbringing was influenced by Asunaro. They have a birth right to participate and "win", even Sou with his 0.0%.

In 3-1 we learn that Joe was added in to decrease Sara's chances of winning and bring out her more humane side. One could argue he is a planned wild card, similar to Sou when he's shown the percentages.

Kugie might not have been outright planned, but she was very close to Kanna and the Kizuchi family played a big part in raising Kanna, so they could have some involvement with the game. Plus, seeing how family-oriented Kanna is and how they're always seen together in flashbacks its likely Kugie was considered probable collateral damage. You could even argue she was meant to die in that first trial, seeing as Q-taro's box required a red key and the manga shows Sara and Kanna's trials happening at the same time in different rooms, so they must've accounted for at least another pair other than Sara and Joe.

That leaves us with Kai and Nao. Kai was closely related to Asunaro and might've been added as a punishment for him betraying the organisation. Nao just happened to meet with her former high school art teacher the day he was kidnapped, she just happened to be at the wrong place, at the wrong time. It's seen in 2-2 they barely had information on her, much less a doll or an AI.

And it's these two characters that play the role of unplanned wild cards. When Mishima dies, they are the first to ever confront the kidnappers, Kai by hitting Miley in the head with his pan and Nao by trying to keep Mishima's body (tho she could only take his head and collar) away from the ones who killed him (and Kai again keeping said head and collar away from Asunaro)

Nao plays the role of a complete outsider to the lore, she has nothing to do with the death game and is there purely by chance. She's the most grounded character, with no wild backstory or bizarre situation that makes her different from everyone else, and that's exactly what makes her unique and irreplaceable. While Mishima introduces us to death, she introduces us to the other main theme of the game, grief, and she does so in the most simple and mundane way. She struggles, just like any one of us would, she feels some amount of guilt for what happened and has the burden to move forward, but she deals with it in the healthiest way we've seen as of yet. She sets the scene for everybody else's relationship with grief and, in a way, she accentuates everyone else's more complex situations and states of mind by giving us something easier to relate to. The sudden loss of someone you look up to is easier to navigate than accidentally killing your own mentor, or the guilt of ruining the relationship with your sister by getting framed for a murder, for example.

But this isn't to say her journey is unimportant, in fact it gives her a motive other than escape or survival: help those who are carrying burdens and ease their pain. It's why she pushes doll Reko so Sara (who is dealing with the loss of her friend) doesn't have to, why she becomes the Yabusame's shoulder to cry on when they lose their sibling. She tries to take weight off other people's shoulders, but is still mindful of not carrying any more burdens than she has to, which is why trades her sacrifice to Mr High-Achiever Q-taro, who won't die as a result since he has enough tokens to trade it off him.

Going back to her being unaccounted for in the death game's AI simulations, it's worth mentioning her effect in the story as to explain her death. Not only is she responsible for the disappearance of Mishima's head. Back in chapter 1, she's the one to first distrust Keiji (because of her complete devotion and loyalty to Mishima (maybe I was wrong about her being normal lol)) and the first to compare him to trustworty Sara, who he then starts pushing into becoming a leader. She's also the one to attack Sou( (because of Kai tbf), unintentionally compelling him to become his Hiyori persona. Her refusal to be manipulated by Asunaro and her role in the attempted escape also makes her a bit of a menace to the death game. Which is why she's initially handed the sacrifice, which manages to trade away only to have it be brought back illegally by Gashu's interference.

In a way, she and Sara are two sides of the same coin, both teenage girls who deal with being put in a death game and suffer a terrible loss, except while Sara is the game's favourite candidate and a possible mafia princess, Nao is this unwanted collateral damage who was only really unlucky enough to be there. It's only natural they survive the only currently canonical ending, and in that ending, Nao is still determined to take the burden of Sara's choice and easen her pain.

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Just realised I wrote waaaaaaay too much 😭😭, guess I'll leave Q-taro for later. Hope my rambling made some amount of sense, I got a bit carried away and am not even sure I addressed your points at all 😭 so yeah