1. Not just anyone can float a global currency.
2. The volume of currency must be massive - large enough not just to lubricate trillions of dollars of economic activity that takes place on the other side of the world, but so large that ordinary transactions and business fluctuations do not effect the currency's day-to-day value. Otherwise, instability would scare users away from using it.
3. The provider's external trade must be so small relative to the size of its home economy that day-to-day changes in the currency's value don't dramatically upset the domestic economy.
4. As an extension of that, the provider must be so unconcerned about the currency's value that it doesn't (unless there's a really big disruption) intervene in currency markets to push its value up or down. Again, if people are concerned that the currency is going to be manipulated once they start using it (and therefore are reliant on its use), they aren't going to adopt it in the first place. I.e your first paragraph is correct.
5. The provider must be willing to let the money flow at the whim of everyone else - if they can't get their hands on it when they need it, they're not going to use it.
6. And last but not least: The provider must be able to secure the very global trade for which the currency is used.
7. Some 70% of global currency (by volume) is in some way linked to the USD. The USD is used for over 90% of global trade and of that tiny 10% left over, iirc, 90% of it done with the euro in the eurozone.
8. This is NOT going to change. The whole planet uses the one currency for the same reason everyone within a country uses its currency: Everyone use it, because everyone use it.
9. I can't remember the exact numbers off the top of my head, but there's several times as much USD in circulation as the U.S actually needs domestically. I'm exaggerating to make my point here but if we were to assume it was 20x as much (i.e that the yanks only had/used 5% of what's out there) then they could print twice what they actually have and only debase the currency by 1/20th.
10. Hence why they can "quantitatively ease" eye watering amounts of "stimulus" into the system and have absolutely SFA consequence for doing so. Hell, last I checked, the last batch of stimulus was overwhelmingly not even printed - it was mostly borrowed by the U.S government at rock bottom interest rates as everyone were trying to get their money out of the rest of the world anyway and so loaned it to them for peanuts. They don't even need to print most of their (massive) stimulus even now.
11. That is the degree of penetration & confidence the USD has and it is absolutely unique to it for a reason.