The problem is that now all the money issued by countries is fiat after the United States went out of the gold standard in 1971 which means that if the main fiat currency around the world the dollar were to collapse that could in theory collapse the entire economy of the world.
Yes, most currencies are explicitly, softly, and/or unofficially pegged to the dollar. This is because the world system ensures (in effect) that every financial system is weaker than the US system. (And yes, that includes the euro!) The pegging is done by by non-US elites because it helps create confidence in the currencies they issue.
But, when the dollar is in real trouble, there is no inherent reason why these currencies can't stand on their own, if their countries can keep inflation in check.
Another thing to remember is that currency collapse is not the same as economic collapse. The 1923 Weimar hyperinflation completely destroyed the German currency, but the economy was back to normal as soon as a new stable currency was issued before 1924. Yes, there were big winners and losers, and it was not good, especially to those who kept believing in the paper money and kept most of their savings in it, and were too old to work after the stabilization, but it was not the end of the world for the economy or the country as a whole. (Hitler's rise came only later, after 1931, during the Great Depression, which was a deflationary problem.)