I think they did show that James turned into a good man.
First by the fact Lily ended up with him when she wouldn’t have anything to do with him in her younger years. He clearly outgrew whatever spoiled or obnoxious tendencies he had when he was younger. He becomes “Head Boy” without ever having been a prefect and it’s understood he really cleaned up his act in all areas.
Then by his treatment of Remus, who he not only befriended and protected while in school, but financially supported as an adult because Remus couldn’t get work when it was known he was a werewolf.
James also had very strong principles and was outraged at Snape’s willingness to use racist language even against his “best friend” Lily. When Voldemort tried to recruit James he wouldn’t have anything to do with his ugly philosophies.
Most of James sins are against Snape, but that was a two way street. Sure James was arrogant and sometimes mean spirited but the hexes he would use against Snape were ones Snape created himself. Snape hated him even as an adult but James saved his life in school risking his own to do it. And while it’s never good to bully anyone, if you put it in modern terms would people feel the same sympathy towards Snape if he were in some Neo-Nazi group? That’s really what he was involved in.
By the time James had matured he was willing to sacrifice everything for his principles and his friends. Snape willingly joined with Voldemort and only broke with him because of his feelings for Lily, not because he saw him as wrong.
While we see a scene entirely unflattering to James from Snape’s point of view we never get to see one from James regarding Snape.
As an adult Snape picked mercilessly on the child of his old rival to get his revenge and still tried to ruin Remus’s life because he had an incurable disease. James died a hero for a cause and protecting his wife and child.
James clearly had his flaws when he was younger which were exacerbated by older, indulgent parents but he was at heart a good person and improved as he aged even dying young as he did at something like 21 years old?