I think basic points all made but maybe not at once:
-A single fiat currency without a single govt means the constituent govt’s in the currency can’t set their monetary* policies in line with their fiscal* policies. Monetary policy is determined by the central bank which controls the currency with each govt only influencing that in proportion to their influence in the whole set up. Fiscal policy is still set by the national govt but at least indirectly constrained as the currency union inevitably tries to reduces the tension between collective monetary policy and individual national fiscal policy.
-Related, maintaining the integrity of the multi-national fiat currency tends to put the more fiscally responsible countries indirectly at least in the role of credit guarantor for the less responsible ones.
These are the two reasons the Euro is at best a non-disaster and hardly something the rest of the world is champing at the bit to emulate, especially with much less economic integration (free movement of goods services [much less true in Eurozone than goods], capital, people, etc) across the globe than within the Eurozone.
One way around the second problem is a gold or other non-fiat global money standard. In the classic gold standard period from around 1880-1914 there kind of was a world currency, gold, in that a very large % of world GDP was in countries (or their colonies) with currency values fixed to gold and therefore to each other. You had to exchange USD for GBP, but the rate was always USD 4.867:1GBP so the fact they were nominally not the same currency made less difference. Although, both govts maintained the right to break that relationship as the US did in the Civil War (rate went up as high as 10) and the British did in WWI (sank to 3.66), which was much easier to do than breaking up an actual single currency.
Anyway, gold based money doesn’t solve the first problem. But it’s fair to recognize that fixed exchange rates, via a gold standard, do largely achieve at least one thing which is billed as a positive aspect of the Euro, eliminate or at least greatly reduce exchange rate risk, and you generally assume there’s some cost to any risk. There’s just other problems fixed rates cause, plus again the risk of changing exchange rates doesn’t go away, it just would happen in big jumps when a country in the system is forced to drop out. The good news/bad news of a system like the Euro is how colossally expensive it would be for all concerned for a major participant to drop out, which makes everyone work harder to avoid that, but doesn’t mean a big chronically slow growing fiscally profligate member (ie Italy) won’t some day still have to drop out, and it will be a real shit bomb if they do.
*one might quibble about dictionary definitions of these two terms but in common usage in finance and economics, to take the US as example, monetary policy is what the quasi-independent Federal Reserve Bank does in setting interest rates and money supply, fiscal policy is what the legislative and executive branches do in setting spending and taxes.