Well, the reality is that letting the barbarians in actually did in significant part lead to Rome's downfall. They rampaged through the countryside and sacked Rome multiple times.

Rome was in a state of near perpetual warfare with the Germans for centuries. Eventually Rome became too weak to defend its northeastern borders and the Germans hollowed out what had become a rotten western empire.

I don't know why you're being downvoted - the analogy to modern politics they are trying to push is hilariously bad. Are we really blaming the Romans for not supplicating the Goths and then getting massacred by them, leading to a 1000 year technological stagnation? Are we really trying to project Donald Trump onto Marcus Aurelius? You've got to be kidding me.

No, we're projecting Donald Trump onto a hypothetical Roman politician imagined in 2009 by Ugo Bardi the Oil Drum writer, due to the coincidental and quite obvious similarity of their "wall" platforms, including both the expense and the futility, as well as the fact that both are set in empires collapsing under their own weight. Is it so hard to see?

America isn't an empire, and is hardly collapsing under its own weight. It's actually doing incredibly well, aside from some annoying partisan bickering.

That is, as they say, the naive view.

Interestingly, the Gothic rebellions that lead to the sacking of Rome twice in the 400s AD was a direct result of the Romans abandoning their traditional policy of integration, dispersion, and resettlement in favor of abusing and exploiting the desperate Goths. Given a choice by the Romans of starving to death or selling their children into slavery, the Goths chose 'none of the above' and went on a rampage that led to the position as a coherent military power within the borders of the Empire but not truly tied to it.

The degree to which the Romans relied on barbarians in later years for their own defense was quite significant -- and they rarely afforded barbarians full citizenship.

By the time Rome was sacked by barbarians, it was in terminal decline anyway.

Walls being useless in one situation at a given time and place does not mean they are always useless: for instance the great wall of China have been really useful to keep northern barbarians at bay for centuries.

And the walls surrounding Constantinople kept the eastern Roman empire going for an extra millennium after the western part fell.