Considering historical events get explored in fiction all the time, I have no issue at with the retelling of a story like this. I agree with you that you can explore things through fiction that you can't through pure fact.
A story like this is an interpretation of a passage in the Bible; the difference between this and a thesis on a book of the Bible is fiction can make you feel the story, meaning you get just as much or more from the story then you would from a academic paper. Plus you don't put people to sleep this way.
I have actually toyed with doing a re-telling of the Christmas Story, but setting it in the future. My thinking is if people read it and are intrigued by the source material, they may want to seek out that source material. I thought of the idea while sitting through yet another re-enactment of the Christmas Story last December (my wife has been teaching at private Christian schools the past 5 years, and I have to go to the Christmas Program each year). Or even if nobody else reads it, it would be a way for me to explore the story further myself.
~Hat~