Because it doesn’t serve to advance the plot to kill her immediately. If she were going to be killed a few minutes into the movie, then why bother having her there at all?
It’s the same as why doesn’t the Bond vilain just kill 007 as soon as he’s captured instead of talk talk talk followed by some contrived torture from which he (of course) manages to free himself?
Basically the same situation. A quick efficient death does not serve to further the plot. And that’s what movies are all about.
Delaying the death of the hero (heroine) is a time honored plot device which is as ubiquitous as the upset scattered fruit cart in the chase scene of an adventure movie.
Have you ever noticed how many fruit carts are so conveniently located in the most awkward places so that they will certainly be turned upside down in the course of the chase sequence with produce flying everywhere?