For my own work, I don't see a point in including any kind of story. They would pretty much well all be the same anyways:

"Well, I was walking down this alley and the textures of this wall/collisions of opposing materials/placement of the piece of graffiti grabbed my eye."

I guess it all comes down to the subject matter as to whether or not a story fits. As well, it would be up to the viewer as to whether or not a story is wanted. Personally, I generally don't care what the story is behind the photograph. I want to experience the photograph as it is, unbiased by anything else. If the photo can stand on it's own, without a backstory, that is a quality image. If it needs a story to have a full impact, specifically if the photo is alright, but the story makes it seem great, then I think the photo needs some work.