Was reading tv tropes because that's what I do when I'm bored and Kotoko is.... Just REALLY tragic hero coded. Let's get into it.
"The truly tragic kind of suffering is the kind produced and defiantly insisted upon by the hero himself so that, instead of making him better, it makes him worse and when he dies he is not reconciled to the law but defiant, that is, damned. Lear is not a tragic hero, Othello is." - W. H. Auden
Kotoko sets out to do something heroic (Saving people, avenging people who cannot avenge themselves, that sort of thing), but makes herself suffer more by doing so to the point that she falls apart and the goal deteriorates. "Instead of making [her] better, it makes [her] worse".
The tragic hero is a longstanding literary concept, a character with a Fatal Flaw (like Pride, for example) who is doomed to fail in search of a Tragic Dream despite their best efforts and good intentions.
Mhm, yeah, uh, a character who wants good but ultimately fails to achieve it due to having some sort of flaw? A weakness one might say? Kotoko genuinely wants good, but due to simply having flaws and, from her perspective, weaknesses, she cannot achieve what she wants to or twists her goal in some way.
A Tragic Hero can work as a protagonist or an antagonist. As an antagonist, their goals are opposed to the protagonist's, but the audience still feels sympathetic towards them.
We ssee Kotoko as the "protagonist" via her own MVs, but we also see her as the "antagonist" to other characters. Shidou, for example, wants to save people in order to preserve his own purpose and Kotoko wants to deliver justice in order to preserve her own purpose and... I have yet another post to probably make at some point in the future about Shidou and Kotoko parallels. But that's besides the point. Anyways to Shidou Kotoko is the antagonist and is even mentioned in Triage ("To extract that fang, now") and to Kotoko she is the protagonist and a hero saving the weak.
Tragic Hero protagonists usually die, but that depends somewhat on the tastes of each era (they always die in Shakespeare, but ancient protagonists would often suffer a Fate Worse than Death and/or be left to wallow in their pain instead).
Not much to say about this except I believe in the everyone/some people are dead and if it's true this applies. Also, with whatever happens to Kotoko in T3, we could possibly consider this a "left to wallow in their pain" type of deal.
Aristotle only says that seeing a prosperous person fall is a good source of pathos, and that it's more pathetic to see a not-entirely-bad person suffer due to a mistake than to see wholly good people suffer for reasons beyond their control.
Doee this count as "Kotoko is the weak she looks down upon"? She is not pure and is flawed and fell to temptation via her own vengeance and/or a drawing towards violence depending on what you believe about her. She is weak, and she is not a good person suffering for reasons she cannot control; she's a complicated, messy person suffering for her mistakes.