>In contrast, it would be a terrible thing to forcibly lock people into their birth countries to stop brain drain.

This isn't hypothetical, of course. This is how places like the Soviet Union and East Germany worked. It was policy to literally shoot people trying to leave the country without permission. On the other hand, while certainly not justifying this atrocity, there certainly has been a "brain drain" as engineers, physicians, and scientists from the former Eastern Bloc have moved West for better employment opportunities.