Certain European filmmakers, Federico Fellini among them, became famous for the improvisational quality of their movies. However, even these renegades from the traditional studio system relied on scripts and detailed production plans. Within the limits of predetermined locations and situations, these directors permitted actors to vary their lines and actions, achieving a feeling of spontaneity. But that's not the same as shooting without a script.
Even “unscripted” projects like documentaries need some kind of script, though it might be just a shot list or storyboard.
Why use a script? Professionals all know why—three big reasons:
It's a way to evaluate your story before you shoot it. It's easier and cheaper ...