I didn't get that her daughter's disease was a direct result of Louise's interaction with the spaceship or the aliens. In fact, for me at least it didn't matter. Kids die of rare diseases every day. It was her smile and peaceful acceptance of her path (both good and bad) that led to her cherishing every moment her kid was on this earth. As this realization was unfolding, the film went from science fiction to spiritual.
The fog and murky atmosphere of the aliens represented the idea of uncertainty, of being completely in the present, neither rooted in the mistakes of the past nor fretting about the challenges of the future. It's awareness in the moment. One can certainly lean in the present when the burdens of the future are already revealed. In fact, I believe it's purposefully not revealed if she could change her decisions or the future. Again - fog, murk, uncertainty. It doesn't matter. Her realizations around the language only become clear when she is face to face with the aliens in their murky, foggy uncertain atmosphere.
It's a comparison between the hard linear demands of science versus the soft, uncertainty of the spiritual (and here spiritual doesn't have to mean divine) there can be spiritual implications in nature - no god needed - just feeling the interconnectedness of life can be spiritual. Being in the Tao, in the flow.
For me at least - that was the big payoff. There can be a natural connection between those two worlds: science and the spiritual and also that words do matter, they matter so much that they can change how you interact with the universe.