Rome fell for many reasons, but immigration was surely one of them. The schoolbook notion of "Barbarian Invasions" makes many people think of armies sweeping across Europe, defeating Roman soldiers. Sure, there was some of that. But mostly these were migrations of entire peoples.
Peaceful Germans moving into France were not always seen as a bad thing. Give them farms, and they won't start trouble. They want to join the army? Great! Rome needs soldiers. They are gaining positions of political power? And they don't speak Latin? And they worship strange gods? And they don't understand why the emperor isn't a German?
Well ... the social contract gets mighty frail when the outsiders just won't assimilate and then start to think that the host society needs to start making changes.
History will look back at our times and it will classify this as a time of Migration and Invasion. Mexicans into the US, Muslims into Europe, Chinese into Africa ...
All the old concepts of national borders are breaking down. This facilitates One World Government and it works against the idea of national self-determination and personal freedom.
In the end the Romans came in and it was vini vidi vici all over the place!