Here's why:
* No Romantic Development: The third film focuses on the epic battle against Sauron and his forces. There's little time or space for romance. Kili's focus is on the fight and his impending death.
* Tauriel's Ambiguity: Tauriel's character remains somewhat ambiguous. While her affection for Kili is clear, her actions are driven by her own sense of duty and loyalty to Legolas. She doesn't fully reciprocate Kili's feelings.
* The Tolkien Canon: Tauriel is not a character from Tolkien's original *The Hobbit* book. Her inclusion was a decision made for the movie adaptation.
Therefore, the love story between Kili and Tauriel is left unresolved and ultimately fades away with the end of the trilogy.