She may know about war from the memories of the other hosts- that, to me, doesn't necessarily make her a better captain- I don't think her other hosts were, and she wasn't slated to be joined. One of her hosts was a serial killer for that matter... and I'd personally resent a simple "get over it" if I got 3 people killed. Kedair is right, Dax has a terrible bedside manner. May... maybe I wouldn't have minded what was said if it was a friend of Kedairs... that wouldn't be so bad. I doubt this is over...
She may have won, but thats not something she's going to be able to pull off very often, Captain or no... or I venture to say its not ideal...
I am also sure that this isn`t over. It was just a start, giving Kedair a chance to look at what happened from a different perspective and giving her a crutch so that she could function during the crisis.
Now that the threat is over, I agree that Kedair needs proper treatment. Dealing with a trauma takes a lot of time and she will need support.