They pay regardless of the country they live in. The standard in European countries is that you’re only considered a tax resident if you spend a certain amount of time in the country per year. It’s easy for a wealthy person to avoid paying taxes in Europe, but an American can never avoid it, regardless of residence.

And again, just because they move to a state with lower taxes doesn’t mean they don’t pay taxes. The highest earners in the US pay the vast majority of taxes. This is a fact you can easily look into yourself.