In my idea, I believe that if a country has a currency that is of high value, it will increase her value also in global exchange making it to have more excess in exchange compared to the country with less value rate. That is, if you want to have the high currency, you have to exchange more of your local currency for the higher currency and that strengthens higher currency more while the lower or cheaper currency keep depreciating. Also it will help foster more international benefit and advantage in trade. It will be cheaper for investors from strong currency to import goods and they have more products than what investors from lower rate currency would get when they are importing or exporting from higher currency country.
Factors that can make a particular country stronger based on GDP, economic strength, productivity, politics or other resources because these elements are quite important as an effort to grow the power of a country in making its influence. For economic growth, I might agree because the areas you mentioned have a much better standard of living, but what can strengthen a country may not only be the exchange rate of the currency itself.
The dollar and the euro may dominate but are not necessarily as strong as the currencies you mentioned in quotes with exchange rates, but they dominate the global market even though we know that fiat currencies always have limitations that can weaken them under certain conditions.