Hey, I really appreciate these thoughts. If I could indulge myself and relate it to a personal anecdote: I was talking to my partner about this idea of enjoying sad stories/music. Presenting a 'perfect' character, Mary Sue, or whatever we may want to call them, is typically - not always - representative of a unwillingness to see characters as capable of growth. It is universally accepted that sad stories help us feel understood in our sadness, and so then, broken characters help us understand our own flaws. Reading about a character who feels purposeless in their life does help us understand how losing oneself feels and manifests. I'm a very emotional person and it's very easy to make me cry with narrative, and recognizing what I see as my negative traits in a character is super cathartic, just as seeing a sad ending is.
To an extent, this manga is curious in how this perfect student falters. Touko is actually shown to be kinda scummy and pushy at times - never breaking boundaries, but expanding them like a balloon that so far hasn't popped. She has this idealized vision of herself that is broken by how she behaves around Yuu, and Yuu knows this and teases her for it. Touko's obsession with imitating her sister could also be explained by what you say about fitting into someone else's shoes, even when there is no real need or obligation. Though, surely more of that will be explored later. Kanou's play seemingly is, at least conceptually, about how a true "self" does not exist, it's all how outside perceptions shape the understanding we have of ourselves, which I really appreciate.