I think that you might be overstating this aspect of Kaladin's character...
I mean, he doesn't want to kill Moash, not just because Moash was once his friend, but because he sees himself in Moash. Moash has lost loved ones because of lighteyes, just like Kaladin. Moash has been unjustly enslaved, just like Kaladin. And I think that Kaladin sees Moash as someone Kaladin might be if he hadn't had Syl. And a friend is someone who's hard to kill, in cold blood or otherwise. There's a part in WoR where Kaladin says, "If I kill a man, I'm going to do it in the sunlight, and I'm going to do it because there's no other way", and killing Moash would have been against that. Moash said, "I surrender," and Kaladin was A, shocked to see his former friend randomly in his hometown just at the moment he was there too, B, exhausted mentally and physically from his nonstop fighting, and C, reluctant to kill Moash because of his similarity to Kaladin. Moash knew just what buttons to push in Kaladin's tired, cracked psyche to make him not kill him.
Kaladin is an amazing leader. He is inspiring and indibnibly good at uniting people, and he's an incredible fighter. And that's why he stayed in command so long: Dalinar knew that Kaladin was, usually, a good enough fighter that he made up for his moments of struggle. Along with that, Dalinar knew that fighting was... all he had left, pretty much. So Dalinar delayed in "firing" him.
He wouldn't normally respond like that. He used to be a better bodyguard in the ways you've mentioned. But years of fighting and loss have taken its toll. He can't really kill, emotionally.
I don't think Kaladin's going to be in charge anytime in the foreseeable future, if ever again. He told Dalinar as much at the end of RoW. Also, I don't think Kaladin was aware that Moash was the one to kill Teft, which is why he didn't hunt him down.
I'm not going to respond to this thread again, because I'm a huge Kaladin fan, and my emotional instinct is to go, "B-B-BUT KALADIN'S AMAZING! HOW DARE YOU INSULT MY BABY!"
Which is not great. So I'm going to avoid that possibility. Also, you might want to avoid using the word coward... I mean, PTSD is a real thing, and it could be offensive...
I know that Kaladin is a well loved character, and so you might not want to be so... hostile, for lack of a better word, on such a controversial topic, I think.
G'day!