Millions more Europeans immigrate to the United States than the reverse — which only makes sense, given how much higher the standard of living is in the United States relative to typical Western European countries.
The typical WE country has more vacation time, a greater safety net, longer lifespans, higher education rates, and consistently trade between each other for "happiest nation", and no gun deaths, and you don't hear much about homeless encampments.
There are certainly reasons for the lack of American expats, but living standards ain't it.
Genuinely amusing how much *some* Yanks see Western Europe as a dystopian hellhole.