Actually if Zuko hadn't gone with Katara and she went off on her own to confront Yon Rah (because are we really gonna believe she would have never confronted this man on her own) she probably would have been more likely to kill him. Without someone to listen to her, to validate her anger and grief, to tell her that her mother was brave, she probably would have been in a much worse place emotionally by the time she had him at her mercy.
Part of the subtext in this episode is Yon Rah having no one in his life, the guy has no family except a mother he hates. Katara realizes that she isn't that helpless little girl anymore and also she has people who will support her no matter WHAT choice she makes (even if Aang doesn't).
Who do you think helped her more, the person who thought the worst of her and talked down to her, or the person standing next to her who helped her through her negative emotions?
The episode just doesn't support a reading that Zuko and Katara's relationship was unhealthy OR that Aang knows better.