LONDON — A cursory assessment might find the United States a less than ideal candidate for the job of managing the planet’s ultimate form of money.

Its public debt is enormous — $22 trillion, and growing. Its politics recently delivered the longest government shutdown in American history. Its banking system is only a decade removed from the worst financial crisis since the Great Depression. Its proudly nationalist president provokes complaints from allies and foes alike that he breaches the norms of international relations, setting off talk that the American dollar has lost its aura as the indomitable safe haven.

But money tells a different story. The dollar has in recent years amassed greater stature as the favored repository for global savings, the paramount refuge in times of crisis and the key form of exchange for commodities like oil.

The enduring potency of the dollar gives force to President Trump’s mode of engagement. It has enabled his Treasury to find buyers for government savings bonds at enviably cheap rates, even as his $1.5 trillion worth of tax cuts added to the debt. It has reinforced Mr. Trump’s authority in imposing his foreign policies on an often-reluctant world by amplifying the power of his trade sanctions — especially against Iran and Venezuela.