Ryan Cooper asked the other day why smaller countries seem to run better macroeconomic stabilization policy, and conjectured it has something to do with the fact that they don't have such large banks. I think this is a multifaceted issue that extends beyond the narrow confines of monetary policy. When the world was more protectionist, big countries had the big advantage of a large internal market. But in today's world I think small countries are generally better-governed and have a brighter outlook going forward.
One reason is that small countries have less incentive to waste resources on prestige schemes. India, for example, can't keep electricity on in major cities but is planning to land a rover on Mars next year. If India was small, it would just be a small poor country trying to improve its shaky domestic infrastructure. But since India is big, it has great power aspirations notwithstanding its poverty. So they want to have a space program. Here in America, logic would say that since we're so much bigger than Canada we could get away with dedicating a smaller share of our national output to the military. But instead we dedicate a bigger share because we can realistically aspire to global military hegemony in a way that Canada can't. China is trying really hard to "win" the Olympic aggregate medal count.
None of that's 100 percent relevant to Cooper's question, but I do think it's plausible to think of a "strong dollar" (or euro or yen) policy as a costly national prestige project similar to a Mars mission or an aircraft carrier or a bunch of gold medals.
Thanks to Kieran Healy for alerting me to the above relevant text.