To nip some arguments in the bud,
1) Catharsis is satisfaction that comes from a resolution. It isn't necessarily good or bad and is merely a story-telling device. For instance, Thanos snapping half the universe in Infinity War is cathartic for the audience, even if it's a "oh shit" moment. It's a story-telling device. Sure, Hamlet stabbing Claudius once with a poisoned rapier and once with an un-poisoned one before making him drink poisoned wine and calling him an "incestuous pig" is probably not mentally healthy, but it's a moment of emotional suspense within the audience during the plot of Hamlet.
It's not emotional stupidity or a lack of empathy. People can distinguish fiction from reality very effectively, and such moments where people feel justified in their actions in a story may be the peak of engagement for that medium, but does not necessarily say that such deeds are moral or even good if carried out in real life. Sure, these behaviors are unhealthy in real life, but that doesn't mean that it's a flaw with the work that a character is unhealthy or that the work is endorsing their behavior.
In the case of MC, the work pretty much out-right vilifies him and shows what he does as being outright vile, even if its cause is understandable and we, the audience, can sympathize with him. We're not meant to look at what he's doing for his Vendetta as the best and most effective means of making the world a better place, but as the actions of a man who has fallen so low that he has no other choice.
A great comparison I think is with Arthur Fleck from
Joker. We're meant to see things like him shooting
as a bad thing, but it's a moment of catharsis because of how the scene is framed and it creates a satisfying resolution to an arc. Fleck is also a man with severe mental health issues and who is not considered as being a moral or necessarily good force, but one with understandable motives and a logical through-line, even if it is mentally unhealthy, which Arthur most definitely is.
Your argument here focuses less on story-telling and characterization, but more on how a real-world therapist or psychologist believe that people SHOULD act, not how they necessarily DO. It doesn't matter what studies you cite because we're not debating facts here, but how a certain character internally operates and if it's consistent with what is established.
The issue I see here is that you're trying to enforce a standard that the work is not trying to apply, and that is irrelevant in perceiving how a story is told and how someone is characterized, and what that is meant to do for the story in question. It's immaterial to the universe we're discussing and is ultimately a Red Herring to whether a character is well-written or good.
2) I am not saying that you are not allowed to dislike the main character. I am merely pointing out that, from a narrative perspective, he is well-written and consistent. Subjectively, you may dislike him, but there is nothing objectively wrong about how he is characterized.
Additionally, you may find his actions stupid, but keep in mind what his goals are. They are not to free the nation or help the people, but to get his revenge. Sure, we are meant to find this to be undermining the issue at hand, (i.e. the corruption and genocidal actions of the heads of state) but, in regards to this specific individual, everything he does is so he can better obtain that goal.
He's not Luke Skywalker and the rebels taking on the Empire, or the various resistances fighting the Nazis in occupied territories in the Second World War, but, instead, essentially
Kill Bill-ing his way through the people that wronged him for his own personal vendetta. It is not about anything greater or anything more than his own satisfaction, and he is consistent in that pursuit.
Additionally, you mistake how I say that "he was conditioned to act this way" with "he has not say in the situation." What I was saying was the he has been influenced by the others around him to think that this is the only means by which he can obtain his goals, that might makes right and that he must secure his desires by any means necessary because of it. In the sense that all he's known and seen is tyrants and people who abuse their power and strength to indiscriminately get what they want, it's no wonder he ended up as he did. (Arguably, he actually is a bit more moral in that he doesn't harm those who don't get in his way and tries to help defend innocent people if they're under attack by the people hurting him, as was seen when he paid for the damages to the rabbit lady's diner.) Sure, he does have free will, but that's irrelevant to the discussion being had when what I'm saying is that he's a product of his environment, which has shown him that the only way to get what he will need to survive is to fight for it.
Unrelated, but you keep saying that Keyaru is weak. Could you expand upon that? I feel like that you're not being specific enough and that you could expand upon what you mean. If you mean that he is weak in the sense that he is faulted, or is prone to errors in judgment and unhealthy reasoning, (As he is definitely not weak in terms of his abilities) then it's not flaw with the writing as that's fundamental to creating interesting characters. Every character has their foibles, and that's a necessary part to creating engaging conflicts, or else you get Mary Sues/Gary Stus.
Finally for this section, I will say he DOES have a philosophy, in the sense that everyone has a philosophy to some extent. In his case, it's simple Egoism, in that he puts his own desires and wants above everyone else's at any given time and that he holds his own will as to what is most important to him. Sure PTSD (although that isn't the only psychological disorder he has as he has shown signs of Sociopathy, Depression, etc.) and revenge are major factors in his motives, but they're not the only ones and there definitely are more moving parts at play here.
3)
No, there is a dilemma. That's pivotal to the work itself. Whether it was intended or not is irrelevant in that it still stands as a core moral and philosophical conflict.
Intended or not, by either the characters or the author, is the questions that arise that will be fundamental to your assessment of the main character.
How many bad things can you do to a bad person before you, yourself become just as immoral and twisted as they are? How bad do they have to be to cross that line? Is there a line that can even be crossed? Do the ends justify the means? Does doing the same thing that people did to you to the people who did it just? Does punishing someone for a crime that they have committed in the future justify your actions?
These questions won't have objectively right or wrong answers. Sure, people may generally answer one way or another to them, but there will always be a way to make it so they will have to change their answer or specify it in such away that it generates conflict. That's what is interesting about this setup is that the manga explores a character who has his own answers to these questions and sees how far the logic can go. You may try to handwave this away, but there's no real way you can deflect them because they're issues core to even the discussion we're having now.
To address the last point, we've already established that it isn't his goal to act altruistically. His main motivation is not that he wants to be the most efficient at getting revenge, or help the most people, but rather that he wants to savor each time he gets revenge and setup situations in which he can unleash the full, unadulterated and ironic effect he wants to induce the exact desired effect into his opponent to fit his own sense of karma and ironic justice. And, funnily enough, he is actually, slowly, making the world a better place without intending to. I see no issue with the vast majority of his actions in terms of characterization given what we know about him up until this point. Sure, you may find a more effortless route, but in terms of character, this is what Keyaru would do given his view of the world and what he knows in any given moment or situation.
@criver