I am not sure how "they couldn't stop it" is an argument against migration being one of the major causes of the fall of the roman empire if not the leading one. Other causes being ineffective tax collection, ennemies adapting and learning from roman military techniques, and a general collapse of will, where the brightest and most capable ceased to want to serve aggressively in the army and administration for glory.
it's an intellectually lazy, blinkered thing to say
the empire had incorporated new peoples for hundreds of years, through both violent conquest and people migrating in
= immigration is the only reason there was an empire in the first place, and that it lasted as long as it did - it's not like the Roman Empire was constituted of pure Latin OG Romans, lol. (heck, even their founding myths were that they were NOT Latins - it took conflicts for Latins to be recognized and gain citizenship)
so you can't just cherry pick a single time germanic peoples migrated in (as they had successfully many times) and say LOOK IMMIGRATION IS WHY THE EMPIRE COLLAPSED, it's ridiculous
and even if you insist on doing that, again, what's the takeaway? if your policy rests on there being no migration, in a world where there is migration and there's nothing you can do about that, it's a bad and doomed policy - successful polities are the ones with the ability to roll with and take advantage of it, not the ones that stick their head in the sand in some misguided attempt to remain static and hermetically sealed off from the world
