Making the case for Story Games I: Why make a story when there are so many good ones out there?
All stories demand a degree of involvement, and to that degree we are complicit in its creation. This is most true of written works where we must create all the sensory aspects of the fiction from what we are given textually. It is also true of dramatic works, in that events may be implied rather than presented, and the motivations and emotions of the protagonists must be drawn out by the audience. So I'm not talking about a radical step here. The story we leave the cinema/book with is our interpretation, not simply a copy of the author's intent.* We put some work in to make it real for us.
OK. But you can go further down this road. Do more, make more of it yourself. I'm not claiming this must therefore be a better method, but it is a different one, and so gives you different things back. Think of it as another option to get at story; one you can select when circumstances suit you. To take an example from a different activity, a guided tour is a perfectly fine way to get a sense of the layout and history of a city, but sometimes you just want to stomp the streets on your own with a map, a keen eye, and a willingness to ask a question or two.
Note that you don't need to do it all from scratch. Just as a map can be a good framework for exploring a city, producing story can rely on a system that gets you started. One well-established example is the Oulipo school of writing, which uses generative rules for inspiration and uses constraints to channel creativity (constraint in poetry acts comparably, although often in the service of aesthetics, the sound and feel of the words, rather than to further story per se). Being handed a blank sheet of paper and being told to "make something great" is not going to be a fun exercise for most people. Being told:
Jim came back from the war broken, his dearest friend Gavin lost somewhere out in no-man's land. His respite from his pain is his nightly drunken visits to the picture house. Half-dozing through the newsreels, he is shocked agape when he sees Gavin's face emblazoned on the screen, with the heading: WANTED-MURDER. What happens next?could be the beginning of a great evening.
*What I've presented here is taken principally from a neat summary from John Kim.