And your assertion is based on...what? Many of the books - and in this case, especially the Book of Exodus - are claimed to have been "written down" by first-hand eyewitnesses to the events.
The core issue here isn't when they were written, but rather what is written. I don't know a soul who contests the mundane aspects of the Biblical accounts (city names, birth records, clothing style, etc) but supports the miraculous accounts. It's always the other way around. People are unwilling to accept the historical nature of the book because it carries with it an ethical and religious message as well. So they dispute the former, hoping to discredit the latter. Believing they've been successful, they think they and their behavior are no longer accountable to rules and persons they haven't - and don't - want to obey. That may not be your personal take on it, but it holds true in my personal experience. I would think the opposite of your opinion would be more believable - it would be entirely self-serving and more believable for the "losers" in said events, i.e. the Egyptians, Canaanites, etc., to re-write their own histories to make it appear they weren't quite so thoroughly humiliated by a God they refused to believe in or obey.
In modern politics, we would call that "spin control."
Where have you been? Even the mundane aspects of the Bible have been called into question. For example, there are no records of the Israelite sojourn in Egypt -- no tax records, no business contracts, no bills of sale (all three very common for the time period) -- nothing. Jericho was uninhabited at the time given for the Exodus, so knocking down its walls would've been a moot point. There is nothing in the Bible historically verifiable until the Babylonian exile, which, coincidentally, is when many scholars believe most, if not all, the earlier books were actually put to paper (they may have been bandied about as oral tradition for centuries prior to this).