Reading the comments here is kinda frustrating. I don't think the manga was ever portraying Kai as an outright villain OR trying to "vindicate" him in death and portray him as "right." I don't think it's trying to portray either of them as specifically "right," though I do agree his approach is a bit more "wrong" than Satsuki's.
His main role was showing the multiple perspectives to the ability to see premonitory corpses. Satsuki has a pathological need to save people thanks to the trauma with her mother, so she focuses mostly on the "situation": how they die, and how to prevent the death. The corpses only show up 24 hours in advance at most though, so she's basically living in the moment and acting with a constant sense of urgency.
Kai however didn't have that need, and thus was able to analyze the situation and the overall ability from a less emotional standpoint. Compared to Satsuki, he DID focus more on helping the living, because he looked at how to improve the situation overall to try to prevent those corpses from appearing altogether. Don't agree with him murdering people to do it, but that particular method also came from trauma: he saw Saijou (vice pres) being bullied by their teacher, and with that power balance, he couldn't think of any way to save her than to remove the teacher from the picture. Given the fact that first murder saved her, Saijou naturally saw it as "right" and fed into that view as they got older.
One other key aspect of his viewpoint though: he thought messing with "fate" can have consequences. He outright told Satsuki that he'd seen a lot more premonitory corpses since she enrolled and that he thought "fate is looking for another death" to replace the lives she'd saved. And honestly? I think his theory might be right. His approach of killing off an "evil" person to keep it balanced is still pretty wrong, but... It IS weird how many deaths Satsuki has seen in the span of this manga. It's not just a case of a story being more eventful than reality: Satsuki saw her first premonitory corpse in third grade, and then five years later saw her mother's. So she'd had the ability for at LEAST five years without seeing a premonitory corpse, while in the span of this manga she's seen dozens.
Basically, the situation is more nuanced than one person being totally right or wrong. They're both right and wrong, just in different areas. While he and the vice president are wrong for justifying murdering people, they're right to focus on preventing the corpses from appearing in the first place by improving the overall environment. We automatically think of Satsuki as "right" because saving people is generally morally upright, but she's reactionary and only acts once she sees corpses. She doesn't really think to look at the larger picture unless she sees that person die again, which can have nasty long-term consequences if it's not a one-off incident, and struggles at how to help people outside of literally saving their lives.
One more thing: all the characters are right when they say that Satsuki is saving people so she won't feel guilty. She doesn't realize it because saving people IS inherently good, so it's hard to call it "selfish," but her motive does ultimately stem from her guilt more than altruism. And we've seen how that can make her tear herself apart even more when she fails, girl's living on the edge of a breakdown at all times.
