(Unless you're suggesting that salaries are so disproportionately high in the USA that you can move here, pay all of your German taxes, and still be better off. In which case, I have to ask: what the hell is wrong with economics, and why is it leading to this obvious inefficiency?
I suspect the real answer is: "you can't actually do that.")
Seems far more likely that someone would leave Germany, earn a higher salary in the US for a while, and return as soon as a serious health threat made the disadvantages of the US system clear.
Presumably Germany has some sort of system to tax imported wealth to handle these scenarios.
(Immigration bureaucracy, distance from family, working and living in your second language, navigating an unfamiliar system, immigration bureaucracy, and the risk of being arbitrarily deported)
Therefore the "free rider" effect definitely exists, but I don't think it is a huge problem, because the numbers of people migrating out and in again are not that high.
Germany in particular gets a lot more economic immigrants than emigrants so it probably adds up as positive or neutral.