Well, he does snap right into action when there's evidence of survivors. Prior to that, he's prioritizing dealing with the Enterprises "own sick and wounded first".Though I'm always weirded out that he just ignores the distress signal at the start, that's just very un-Starfleety in retrospect.
Which is interesting because one of the most common criticisms I see of TOS among newer viewers is that it deals too lightly with lost crewpeople. This episode could be said to be the opposite extreme...here Pike is having a crisis of confidence and is heading back to a colony planet with his tail between his legs because of three dead and seven injured. Kirk would have been on to the next mission.