So, yes, a country that has experienced a collapse of its currency has few routes to a strong currency other than a strong economy ... but even then, the choice to have a stronger currency rather than stronger demands in labor markets is a policy choice made in the context of a strong economy.
However, a country that has had a strong economy, and in particular a country that has had the strongest economy in the world, can have additional routes to a strong currency ... just as one abstract example, a tacit collaboration with nations pursuing neo-mercentalist policies of a steeply discounted peg against "such a currency" (cough US$) would be able to maintain a higher indirect exchange rates for "such a currency" than otherwise.
That's not a permanently sustainable policy, but its sustainable over the medium term ... for example, over the long term the other parties to the game may not find themselves either able to sustain the neo-mercentalist policy against political demands to deliver standard of living gains, or willing to hold the accumulation of foreign exchange reserves denominated in an artificially inflated currency.
So, US$0.05 (€0.04 soon to be €0.02) version: a strong economy permits a country to sustain a "strong currency" policy, in service to its wealthy or in service to foreign adventurism (or both) ... but a "strong currency" policy without the backing of a strong economy is a foolish policy, and the policy that the US has been pursuing as if having a "strong currency" magically creates the strong economy that is required to make a "strong currency" policy sustainable. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.
a "strong currency" policy without the backing of a strong economy is a foolish policy, and the policy that the US has been pursuing as if having a "strong currency" magically creates the strong economy that is required to make a "strong currency" policy sustainable.
Of course, whether it will or not, that is always an open question, but I reckon it can be done. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.