i think that it was less Kirk going after Mitchell to get Mitchell, and more Kirk going to attempt to rescue Dehner.
Kirk would not have realized that she had "turned," and could easily have thought she had left with Mitchell unwillingly.
Otherwise Kirk and the ship would have simply left, and proceeded with the plan to irradiate the planet later.
Oh yes, I had forgotten that Kirk had been unconscious during Dehner's "departure".
A classic "damsel in distress" scenario, very palatable to audiences of the 1960's.
Elizabeth Dehner might have even read telepathically Kirk's noble intentions and then come to realize, despite her intoxication with her new powers, that something wasn't "right" about the whole situation and eventually came to her senses.