America was complacent about its technological dominance until the Soviets’ 1957 Sputnik launch woke us up. Recent developments in digital currencies similarly threaten the dollar’s dominance, and Washington policy makers are taking notice.

Significant actors, including central banks and social-media platforms, may launch new currencies in the next few years. As their networks grow, they could eventually erode the dollar’s status as the most popular currency for international exchange. Incidents like the attempts of foreign...