So their issue generates revenue for the US state. If New Zealand adopts the Australian dollar, seigniorage is lost to the New Zealand state, but the Australian state's capacity expands. Alternatively, seigniorage signals that the state's control of money and the state's control of public revenue and expenditure cannot be separated, and public finance is an intensely political process. There cannot be monetary union without some significant degree of political union. Note the implications here of the case for US dollarisation - where there is no political merger with the US, a substantial range of national economic policy tools are lost in the dollarised countries.
Seigniorage is lost as is any involvement in setting interest rates.
George W would all but set social and economic policy in Australia. Arguments about complete global dollarisation present the extreme case of the dilemma. There is, for accumulation, a clear logic in having a single global currency. Multiple currencies are as sensible as different rail gauges and different power sockets - they are an anachronistic inconvenience and costly. But where that global currency is one nation's currency writ large, there is a fundamental contradiction.