In my niece's (relatively rural) US high school class several students decided to attend university in Europe with no family ties to the countries in question. It was pretty common in my generation to see, as you note, kids moving to Berlin etc after their studies, but this strikes me as relatively new. Anecdata that seems supported in some of the public numbers [0].
[0] https://www.forbes.com/sites/michaeltnietzel/2025/07/21/reco...