Why did Hamilton believe the US needed to pay off its debt?

Answer 1

He said "Credit is the whole thing". WIth credit, a nation can acquire capital when needed to grow the economy or to defend itself. Without credit, debt stagnates the economy and doesn't earn the respect of other nations, which in turn tempts them to attack or take advantage of a nation's weakness.

To develop good credit, the lenders must be convinced that debts will be paid back. Hamilton was right. The U.S. became respected and the economy benefited from the bank notes offered.