> ... everyone ELSE agrees to accept them for goods and services. It's circular.
If you think about it, there is nothing circular about US dollar's supremacy. If you reside in the US, you are bound by the Legal Tender law -- meaning, by law, you have to accept US dollars as a valid payment for meeting financial obligation. The US dollar is also the defacto reserve currency of the world. All important commodities, for instance oil, are priced and traded in USD -- though there have been a number of bilateral agreements between oil-producing nations and consuming nations (eg, Iran-Turkey, Russia) to breakout of this, the USD still rules the day. If you want to understand how the US dollar became the reserve currency of the world, you do necessarily have to understand the WW2 (ie, military conflict), the Brettonwood agreement that came after the war, the collapse of the agreement in the 70's, and what US has been doing militarily and diplomatically to maintain their dollar hegemony since, but, in short, it isn't just about some arbitrary blind trust in the US dollar by the world (or circular reasoning) that we ended up with the system that we now have.
> How is the might of the US military relevant here? If you lived in South Korea, would you accept the South Korean won, or would you refuse your salary because their military is too weak compared to the United States? I would take my salary in South Korean won because all of my neighbors and strangers will take it in exchange for goods and services. Circular.
IMO, this is a terrible example to demonstrate your point. In case of national security threat or economic crisis, it's not uncommon to see smart monies fleeing to gold or other safer currency (eg, Swiss Franc, Japanese Yen, or USD). South Koreans are less likely to hold their own currency if the US decides to withdraw all 30K US troops and break any agreements in place to militarily assist the South in case of military conflict.