One of the great outcomes of it was that when my wife or I heard the girls say interesting things about their social dynamics at school (another child getting picked on, kids with "fancy shoes", questions about kids with different-colored skin, a new kid to the school, etc.), I could weave those situations into the narrative. It gave us a safe space to explore the issues, and to help the girls process various lessons in an enjoyable way.
Eventually, we moved on to audiobooks and then the girls reading to themselves. But what started out as frustration at a "long" commute ended up being one of the highlights of the day.
[0] http://www.radiolab.org/story/153809-rules-set-you-free/
One of the few differences is that the story is usually finished within said few hours, and a new one begins next week, unless it's considered interesting enough or needs a continuation.
I believe that it's a wonderful idea to do this in general. It exercises creativity and thinking, et cetera, and it's fun to do. :)
s/every kindergartner/everybody/ :P
Eventually I put him in my stories too -- he was member of the Omega Force. At some point he didn't like how his character was acting in the story, so he began to tell me what his character should do. Well over the course of about a month we now do a full on role-playing game on the way to school. The level of role playing matches nearly anything I did when I played D&D. He now leads the Omega Force and I lead the Alpha Force. His squad is larger, but mine is more specialized.
That 25 minutes of rather sophisticated verbal interaction is pretty incredible. I can weave in interesting scenarios and discussions, and the level of engagement is great. I have no data to support it, but I feel like its something that almost every kindergartner could benefit from.