The United States is one of the few countries on Earth that taxes worldwide income. While this sounds scary, it means nothing until you make "real" money. For 2019, the first $109,000 you make are exempt. The majority of people never make it to that point in their lifetime. But let's say you make $250,000 per year. After Australia taxed the sh*t out of you, you may have been left with $150,000 take home. If you file a US income tax return as you are supposed to do as a US citizen, Uncle Same would take you on the difference between $150,000 and $109,000, meaning on $41,000. The income tax on $41,000 is $6,426. Lesson to be learned: once you make about a quarter million a year, invest a $1,000 bill on a good tax professional, who then converts your "income" into investments so that they won't be income to begin with.
Unfortunately, the US now tries to get a stronghold on all US citizens living abroad, because very few actually file an income tax return. Once you tell your bank that you are a US citizen, they'll have to report your bank account to the IRS. But, again, until you make about a quarter million US$ ($350,000 Australian Dollars) per year in income, this is a non-issue.
And once you make $10,000,000 per year, your accountants and tax attorneys will simply invest a great deal of that money, so it won't be income. Warren Buffet, the richest man on Earth, pays very little income tax, because he doesn't take home a billion dollars a year. Why should he, as there's no way to spend it anyway. He simply keeps his "income" at a level that is consistent with his spending (and if you have corporate jets and corporate helicopters you don't spend much personal money anyway), and the rest he reinvests.
An immigrant from Europe, I live on the American Riviera and work as an attorney in Santa Barbara, California.