Why is the Burr vs Hamilton Duel important?

Answer 1

When Hamilton was shot and killed, the young United States lost what was probably its most brilliant financial mind, as well as the strongest leader of the Federalist Party, one of the men most responsible for the passage and ratification of the U.S. Constitution, a fine lawyer whose writings in the Federalist Papers are still referred to as guide to the meaning of the Constitution, and as one of the youngest of the Founding Fathers, someone who would likely have had a substantial influence on the history of the U.S. for several more years. President Thomas Jefferson and his successors James Madison and James Monroe faced far less effective opposition politically than they would have if Hamilton had remained alive.

Although Burr did not die (Hamilton did not shoot at him), he effectively killed his own political career. Burr was also a major political figure in the U.S. and in fact had tied Thomas Jefferson in the Electoral College in the Presidential Election of 1800. (Hamilton's influence threw the election to Jefferson.)