So your definition of a monopoly would be to not have anyone issue other currency except for the dollar, anywhere on the planet? If I was given the privilege to be the only carrot salesman in the US, I wouldn’t have a monopoly because you can still order carrots from France?
You really don’t think the privilege to be the only national organization allowed to engage in banking counts as a monopoly?
In today’s world with technology the way it is, currency is pretty fluid. Insofar as it’s not is just a function of practicality not coercion. Dollars work fine right now, so nobody is exerting any effort to work around them. If they changed, then people would.
As for banking, it seems like there are a lot of those all over the place in the USA, not just one…