Once you've lured us into a darkened theatre, it's your job to entertain us. Unless you specifically advertise that, "No Storytelling Shall Take Place, Only Pretty Images and Disconnected Themes," you're wasting our time. Or at least mine.
I've attended a number of film festivals, screened several independent filmmakers' films as potential movies to use in my classes and workshops, and watched countless hours of films in theaters and in my living room. And if there's one thing that drives me crazy, it's trying to determine the story when the filmmakers clearly had no clue what their narrative was.
Which means that we have a job to do as scriptwriters. We need to tell a compelling story about our character. Returning to an earlier post, we're examining what our character wants and what she'll do to get it. And we're not just tossing random obstacles in her way, but weaving in an equal and opposite-minded antagonist whose own goal will make it difficult or potentially even impossible for our protagonist to achieve her mission.
We also need to know what's at stake; what is the character willing to give up in order to chase her dream? There better be huge risks, or you may bore us. Please don't bore us.
So, how important is story? You tell me. But please make it interesting.