The part with "war so that people know to value peace" is actually not a bad story for him and at least for me not what breaks him.
It's the often used "war to end all wars" trope and tbf. that continent had a massive war 80 years ago. He sees some of his people crying for war so they "can have new trading zones" which is stupid because they have forgotten how terrible war can be. At the beginning I even thought he knew something that we didn't but no.
Is his solution wrong? Yes, but not as a narrative character flaw.
I think you are right with the rest.
Where he falls apart as a character is that they actually ignore his reasons. He completely forgets his reasoning and just does war for the sake of war and daddy issues.
Even that could have worked as a narative like his failing the trials but they failed to use it.
His reasoning was unvorgivable but nevertheless characters use the " we don't have to fight" rethoric and use sad music when he dies.
Even his relation with his son falls flat because it's not really explored. I thought they would go somewhere when he kidnappes him but no, nothing. Not even a silence to imply that he actually cared for him, just ambigous mumbling at his deathbed.
I get what they wanted to do with him and I would have actually liked that.
In my opinion his decending into darkness and failure to live up to his tile would have been more realistic if Wuk Lamat hadn't been so obvious as the victor from the beginning. Gulool JaJa and the food trial were so obvious in their bias that he had no option but to fail. His father didn't even think about him when Wuk lamat and Koana became the new dawnservants. You don't do that as a father, you just don't.
Him seeking new power after we whoop is butt, him hating his son because it reminds him of his father but also having father feelings of his own and being torn in that. This would have made far better writing.