As the EU, a supranational government, strengthened in Europe, it actually made it easier to move to another country. Perhaps if the EU became more and more controlling of its member nations, then it wouldn't feel as if one were moving from another country, because each place would be quite similar in law, I don't agree that supranational governance would necessarily make it more difficult to move to another country.

Also, I think it might be underused right now because it's probably really hard for most people around the world to move to another country for various reasons: financial, social, linguistic, legal, etc.

I agree that moving countries can help people, I think it is currently a huge task for most and ironically, believe that better relationships between countries and an overarching form of governance may make it easier to do.