The view that it was immigration that brought down the Roman Empire does have truth to it, but the idea that the theory can now be applied to the modern West is simplistic.
Peter Heather

Migration & The End of Empire However you line up the different factors involved, there’s no doubt that immigration played a major role in the unravelling of the western half of the Roman imperial system. By the end of the fifth century AD, from Anglo-Saxons north...