I believe you'd need to expect significantly better results elsewhere and/or an easy transition. For somebody with a well-paying job in the US, few other countries promise an equal or better future. For somebody that struggles in the US, transition to Europe for example isn't easy, and it's not like they could reasonably expect to make a lot more money there.
Pretty much everybody from, say, Ghana, can expect to have a better life that is worth the transition in Denmark, but few Danes can expect to have a better life in Belgium that offsets the cost of moving, learning a new language and switching cultures. If European cultures were more similar to the US and there was no language barrier or bureaucratic difficulties, I'd expect more migration, similar to how people will look for greener pastures within their home country.
Pretty much everybody from, say, Ghana, can expect to have a better life that is worth the transition in Denmark, but few Danes can expect to have a better life in Belgium that offsets the cost of moving, learning a new language and switching cultures. If European cultures were more similar to the US and there was no language barrier or bureaucratic difficulties, I'd expect more migration, similar to how people will look for greener pastures within their home country.