Foreign Perspectives on the Dollar
Yes, other countries are conducting international business in Euro. Yes, some of that business used to be conducted in Dollars. But that is only part of what supports the value of the dollar.
The United States is an extremely stable country that is also a huge marketplace. We allow and encourage innovation like no other country, and don't place impediments in the way of instant success. You can get as rich as you want, as fast as you want, if you are smart enough.
Another factor supporting the value of the Dollar is that people all over the world NEED the dollar to have value. First, many non-Americans put their money in Dollars in the United States because they know it will be safe.
Second, you mention the exchange of goods and services in exchange for Dollars. Remember the end results of that exchange: we have their goods, they have the Dollars. If the bottom falls out of the value of the Dollar, it is the the trading partners who will be hit hard, not the U.S. After all, we are not holding those Dollars. China et. al. is. Even China's recent diversification won't change the billions in Dollar assets that make up their wealth. It is China at risk, not the U.S.
Third, the U.S. population has a horrible savings rate. To answer your question, what savings?