The original short story is called Story of your life, as from the point of view of Banks narrating it to her daughter.

No love story, no daughter, no Story of your life.

I suppose you could still have a story about aliens, and the Sapir-Whorf hypothesis, and bootstrap paradoxes, but you wouldn't have this story, and probably wouldn't have the same emotional impact.

It'd be like taking the war out of Slaughterhouse-Five, if we're staying with the aliens and alien-related psychic time travel theme. Or the air out of a balloon.