I'm interested in more of your perspective. I do not think the text reflects true historical events but, I can't help identifying the natural reading of the text which presents as historical narrative. I am open to another reading.
To my ear, the stories in early Genesis have a different sound to them than the histories in Samuel, Kings, and Chronicles. The passages that say "So-and-so, son of so-and-so, ruled over Israel for X years", that sounds like someone trying to create a historical record. I don't hear that in the early Genesis stories.
Also, with the early Genesis stories more broadly (perhaps not with Babel itself), there are the odd ways they don't quite fit with each other. Genesis 1 and 2 tell the creation story in two different orders. The Cain story has Cain worried about the people he will encounter after the murder, even though it seems that the only people alive are Cain and his parents and siblings. The Flood story has trouble deciding whether Noah took 2 or 7 of the clean animals. If we notice those issues, the people who compiled Genesis would have noticed the same issues -- it was their stories, after all. Yet, they chose to include the stories, in the form that we see them. Preserving the stories must have been more important than exact accuracy and consistency to the people who chose to preserve them.
Part of my perspective is that I don't agree with this view of inspiration:
My basic assumption is that the original document was inspired (God Breathed). It is/was without error because God caused human authors to compose the scriptures, thereby communicating revelatory information to humans. This did not eliminate the voice of individual human authors but, rather blended with their voice in such a way that God's word interacts with human culture.
I'm familiar with the idea of verbal inspiration, but I don't agree with it. I see the Bible as a much more human product than this view portrays. My view is the one I described in the earlier post: The people of ancient Israel and the early Christian church experienced God, and they wrote down some stories, histories, and poetry that expressed their encounters with God. Some of what they wrote was historical narrative, and some was poetry or fictional stories or apocalyptic imagery or some other form of writing.
I'll add that it's possible that there are some historical inaccuracies in what the Bible writers wrote down. (I don't think that's what's going on in the Babel story, but it's relevant in other passages.) People make mistakes. And it's possible to read books that have a couple of mistakes here and there, and still come away with extremely valuable information -- we do it all the time, when we read textbooks and newspaper articles and so on.