I beg to differ with your last argument, France and USA have really different approach in how they support citizens, yet both are currently really opposed to let newcomers enter their borders.
I think one problem is like you said, the huge improvement in ones' situation when moving to a new country.
Why is there such a big difference ? Why money is concentrated in so little space and groups of people?
France and the US, while different, both offer far better supports to their people than most of the world enjoys. Social security, free public schooling (admittedly of dubious quality), physical security, etc.