Divinely inspired scripture must be reflecting a divine nature.
A nice sound-bite, but this doesn't actually say anything. In order to make a correlation between the two, you'll have to trot out a litany of assumptions that have absolutely no chance of substantiation. That is, we have no means of identifying or measuring what "divinely inspired literature" looks like. If we had a set of objective, transcendent criteria by which to being the search, the task would be much easier. However, we don't. So then, to say that "historicity" or "inerrancy" or any other criterion *must* be a mark of divinely inspired literature is not only asking a question that can't be answered, but worse sets up a facade that is vulnerable to the most basic of attacks, as a single contradiction can bring everything crashing down.
But the more important point of "inspiration" that should be understood is that such needs no defense. Christians do not cherish the Scriptures and "believe" what they say because they are particularly "accurate" in their history, or uniquely "profound" in their philosophy, or any other external criterion. Christians believe the Scriptures to be inspired because they are "our" book. It is the testimony of the people of God to the history of salvation being worked out within our lives, personally and collectively. They need not be established on any other basis, and I would suggest that any attempt to do so is ultimately doing a disservice (if not violence) to the Scriptures.
A mistake that is not just some copying or translation error is an indication that the original source was flawed.
Why? Upon what basis is this a necessary conclusion? It smacks very much of the biases of modern historical criticism, which itself is based on arbitrary assumptions and biases. You can make this claim all you want, but you have no means by which to substantiate it. Frankly, I don't know why Christians bother with such questions; the Scriptures are our book; they doesn't need to be justified to anyone.
Historicity doesn't prove something is divinely inspired, but a lack of historicity is at the very least a warning sign that something may be wrong, either with the archaeology or with the "scripture".
Why? Upon what basis is this a necessary conclusion? You talk about "historicity" as if it is an objective domain of human knowledge, as if our understanding and determination of "history" follows a set of universal, transcendent, and self-evident principles.
Reality could not be farther from the truth. History, as a concept, has a very high level of plasticity. Not only have notions of historicity changed in terms of the phenomenology of events (e.g., the "happened-ness" of an event, and the means by which to establish the same), but also (and more importantly) our valuation of history has evolved (changed) through each philosophical paradigm shift within human thinking. Therefore, when we link our current philosophical biases about history to our valuation of the "histories" recorded within Scripture, we run a grave risk of silencing the authors of the text and substituting our own meanings and values. This is particular dangerous when our understanding of history makes it difficult to treat texts as we would treat "historical" texts. Since our philosophical biases have gutted us of the ability to value, appreciate, and find meaning in anything that smacks of "myth", we enforce our biases upon the text, possibly transforming them into something they were never intended to be. And all this in the name of "defending" the Scriptures.