While you are right in most respects, the history of Israel is a major part of ancient Middle Eastern history and would be studied as part of our general historical education for its own merits aside from any religious significance.

The rise and fall of Israel, like that of Egypt, the Hittitte confederacy, Assyria, and Persia are part of the story of civilization, and given ancient Israel's strategic location in the lower Levant, Israel's significance was pretty much assured from the time of ancient Israel's formation.

While independent (non-Biblical) references regarding King David are hard to come by, there is evidence that Israel was a major military power and Egyptian ally prior to the rise of the Neo-Assyrian Empire, and I suspect his name would be known today in secular circles.