Granted. Hamilton is only injured in the duel and Burr is shot and killed. Unfortunately Hamilton's injuries severely restrict his mobility and causes other long term health issues. Additionally he finds a sense of renewed faith from his near death experience. Hamilton spends the remainder of his years arguing for a stronger sense of religion in government. Scholars debate if these were actually written by Hamilton.
Several years later, post-2004, Lin-Manuel Miranda reads a biography about Alexander Hamilton and begins work on "The Hamilton Mixtape". While writing Miranda struggles with the awkward later years of Hamilton's life and duel with Burr. Ultimately the story shifts to Washington, then Jefferson and then the Founding Fathers more generally. The Founding Fathers Broadway production is still quite successful, with Miranda's biggest complaints being that it took him far longer to write than he had expected.
As he was unavailable the film Moana is produced without Lin-Manuel Miranda, depriving us of songs like "How Far I'll Go" and "You're Welcome".