Feels like my off the cuff theory from last chapter might be onto something?
I'll cut & paste it here again:
Ch.2 P.19, the charm said:
If we look from the overarching theme/moral of the series that this is Karin learning to accept all the facets of herself through seeing that Yuu, the man she loves, also loves and accepts every and all aspects of herself. The message here is Karin doesn't accept parts of herself and likely believe Yuu will hate some aspects of her; in the mix of Yuu wanting to see her and the charm said it thinks the more the merrier, she did has a say in this shenanigan that she wants the part Yuu doesn't want of her to disappear. After that we also learn from Kumaka arc that it's not only Yuu who has to accept that aspect of her, but Karin herself will have to accept it, too, otherwise she'll disappear. Hence, I reach my conclusion above that the core of this story is Karin learning to accept herself through seeing Yuu accepts and loves all the facets of her.
EDIT
Giving it more thoughts about the magnitude of her wish hinted at in this chapter, maybe her wish doesn't have anything to do with Yuu's and his charm's shenanigan, but purely she went through some traumatic event, doesn't accept herself/hate herself, and probably wish to disappear thinking Yuu will hate what she has become, but it now clashes with Yuu's wish, probably.
Whatever it is, I think the overarching theme still stands that she will have to learn to accept/re-learn to love herself through Yuu.
I've been having similar thoughts to this theory of yours from when we flashed back to Karin's past through the eyes of Kumaka, which showed how the root of her existence is the traumatic disillusionment she felt after overhearing her classmates talk about how self-centered her attempts at friendliness came across to them, driving her skepticism and introversion.
Aika then came with her own flashback in Chapter 9, which seemed to also center on a similar traumatic event involved "failure" to befriend her classmates, but with the details unspecified beyond her reaction to said trauma - namely, ramping up the egotism as her way of putting walls around her heart, and clutching to the idea of being "cool" like she always tried to be in front of Yū.
Of course, so far Himeka and Galka haven't been given flashbacks of similar nature, but some of the chapters where they were the only splinters around did come with some flashbacks that showed child Karin to have already been exhibiting both the "can't be bothered" laziness of Himeka and the optimism of Galka; if we are to assume that they too share the same root for their respective splits as Kumaka and Aika (consistently failing to make friends), then it appears that they represent two different aspects of Karin's response to the trauma: acceptance of her lot in life (because she finds actually doing something about to be too much effort for uncertain gain) on the one hand, and distracting herself from consciously thinking about that miserable part of her life by living in the moment (i.e. being constantly optimistic) on the other hand.
Now, logically, it's implausible for a normal person to react in such different ways to the same trauma all at the same time. What likely happened is that during those years between her original disillusionment with how she behaved and the day her wish upon her charm was realized, Karin went through multiple phases where she tried to cope with her trauma one way, only to find that it didn't work and change to a different way, repeating the process a grand total of 7 times (and thus producing 7 different aspects). And I wouldn't be surprised if the order in which the splinters make their debut in fact mirrors the order of OG Karin's coping phases. That is...
- She initially tried to be apathetic towards the problem, convincing herself that clearly the fault lay with everyone else.
- Eventually the emotional distress became so bad that she forced herself to act optimistic and happy-go-lucky, even adopting gal aesthetics as a method of self-distraction.
- She then fell into a depressive rut where she shut herself from the world and only "talked" to her stuffed toys, during which she finally engaged in introspection that led her to admit that her classmates did have a point.
- Eventually she became angry and determined to prove that she doesn't need to depend on anyone else, and will live up the image of the "cool", confident girl that she tried (with limited success) to present to Yū.
- Presumably, she eventually became disillusioned with the effectiveness of doubling down on the egotism, leading to three other phases that corresponding to the remaining three splinters (including what seems to be a tomboyish phase, if that's what the short-haired Karin on the far left of the original cover is supposed to be).
- Finally, and presumably during the final year of the decade-long separation, Karin gave in to despair and made a desperate wish upon her charm that if she ever reunites with Yū, she would only exhibit the trait(s) that he found/finds likeable in her, and lose all the other, "undesirable" traits. The intensity of her emotions, combined with Yū having already spent those 10 years wishing to reunite with her and the emotion he poured into the wish being coincidentally imbued with his (at the time subconscious) all-loving-and-accepting nature, thus led the charm's tsukumogami to act upon the wish by splitting her into 7 physically identical girls that each represented one of the 7 aspects that she adopted as part of her coping mechanism, and leaving it up to Yū to decide if he really is up to the task of loving all of Karin, or if he will ultimately have to forsake one or more of her aspects.
Ultimately, I feel like the overarching theme is about accepting not just Karin's flaws that led to her apparent decade-long bout of friendlessness, but also the imperfectness of the seven ways she tried to cope with the trauma of said friendlessness, which will likely leave lingering echos in Karin's personality if she remerges back into a single individual. And of course, for Karin to (re)learn how to love herself despite being a flawed person.