Perhaps an unsolved murder would have had negative repercussions for the timeline, moreso than a simple traffic accident--something that would not have drawn attention to Edith Keeler's life work or philosophy. Someone dies in a car crash, you say, "Oh well"; a community activist is murdered and you may ask "why?"
Harlan Ellison story flawed
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In "City on the Edge of Forever", when Kirk and Spock realize the Joan Colllins character has to die to restore the timeline of history, why didn't they just kill her? Why did they have to wait for a truck to run her over? They could've just bumped her off and gone home right away.......