Why restrict it to the nation then? Why not city currencies? There are lots of countries - like India and China - where the gap in income between regions is larger than between countries.

It's a weird concept money, and I wonder what the right level is. I doubt it is optimised at the country level, but then a "better" notion like demographic similarity may be impractical, even if better, e.g. one currency for Northern Italy and one for Southern may be difficult to sell even if preferable, and ditto a unified Basque/southern French currency, or an eastern seaboard Yuan and a country China currency.