Two things on this front. The first is a foreign earned income exclusion. The first $120,000 you earn is not taxed. The second is that one can also renounce their citizenship. It's not particularly extreme if you only plan on returning to visit, rather than live in America, and is quite handy not only for avoiding double taxation, but also making it vastly easier to bank abroad.

America has a habit of making laws that it compels other countries to follow, and banking is definitely one of those. Foreign banks dealing with US nationals have a mountain of paperwork, rules, and regulations to abide to the point that US citizenship is often a substantial hurdle to foreign banking. And, as usual, the extremely high wealth types that acts like FATCA [1] ostensibly target have little difficulty finding ways around it. It's the 'normal' people who get hit the hardest.

[1] - https://en.wikipedia.org/wiki/Foreign_Account_Tax_Compliance...

You make renouncing citizenship sound far easier than it is: renouncing US citizenship is irrevocable. You might have elderly relatives you want to look after once they become too frail to look after themselves; you can't do that on recurring tourist visas. You won't be able to see your relatives for extended periods of time.

(plus you still have to pay outstanding taxes, plus an exit fee that goes up substantially if you make a lot of money; plus I'm pretty sure the Swiss median income, for Tina Turner's example, is higher than 120k USD per year so you're always paying taxes)

Not quite true. The US offers a foreign earned income tax credit for incomes up to $120k (in 2022).

https://www.irs.gov/individuals/international-taxpayers/figu....

That means that for your first $120k earned, if you pay tax on that in your country of residence and meet other criteria, you will not be double taxed by the US.