Is wealth the right term here? I thought it was supposed to measure production, with the actual measurement usually spending (with qualifiers). And, when comparing countries, you have to account for the different currencies. Currencies are typically trade balanced, which gives a rough equivelence for buying power, but that is not true with the dollar because, as the effective reserve currency, it has international demand outside of trade.
I suspect that the US having better investment opportunities than other countries (tech companies for example) might be more important than reserve currency status.
People tend to pay more attention to trade than investment, but investment flows are just as important. A trade deficit often means that foreign investors are buying and a trade surplus goes along with people investing in foreign countries.