Scholars have long rejected the idea that the Deuteronomistic History was written by the characters depicted in the story. Firstly, none were written in the first person, which is how witness accounts are generally written. If anything, they are written from the perspective of an all-knowing narrator writing from a vantage point well into the future.This is a good account of the mainstream scholarly view about the origins of the Deuteronomistic History. There is, as the article observes, plenty of variation in the views held by specific scholars, but most would hold to something not far off from this. I have some more observations on the Deuteronomistic History here.
In addition, had these books been written by different people over hundreds of years, we would expect quite a bit of variation in language and style from part to part (note the differences between Middle English and modern!).
Yet the bulk of these books are written in a uniform manner. That indicates they were written at about the same time, if not by the same person.
Take for example the phrase “to this day.” It is rare in the rest of the Bible, appearing only 13 times outside the Deuteronomistic History. But within, the phrase abounds (multiple times in each of Deuteronomy 6; Joshua 13; Samuel 11; Kings 13). This first of all suggests single authorship. It also attests that the author was not writing about contemporary events but events in the distant past.
I am back from Italy and have a big backlog of stories to post on, and it will probably take me a few days to catch up. I'm working on a brief conference report, but I need to interchange the photos on my various incompatible devices before I can post it. Perhaps this evening.