Nope. First of all, social mobility in the US is not better than anywhere else (https://www.epi.org/publication/usa-lags-peer-countries-mobi...) . Secondly, it's not that much harder to renounce US citizenship than other countries - in fact, in some ways it's easier because the US is the only country I know of that allows you to renounce citizenship without having another citizenship already. My point was only that you don't have to "actively keep" your citizenship, by visiting the US or any other means.