At the mention of the First Servant being chosen by lottery I immediately thought of Shirley Jackson's "The Lottery" and suspected it was headed somewhere grim.
I'd suggest "Charlie X" also. It's not this grim, but Kirk cannot save Charlie from his unpleasant fate.About a third of TOS's first-year stories ended rather solemnly. I don't remember one quite as horrific and grim as this one, though the argument could be made for COTEOF.