When I initially heard it as a teenager, I wrote off the comparison between the US and Ancient Rome as convenient. However, as I got older and started to know more and more people who relocated for work, e.g. to New York or LA, I started to get it. They weren’t going there to become New Yorkers or Los Angeleans. They were going there to practice a trade or profession they couldn’t practice in Virginia, at least not if they wanted to make money.
Same goes for the US as a whole. People all over the world move there for work. Yes, part of that is the “Land of Opportunity” aspect, but equally or moreso is the making money aspect. It’s just a really dynamic marketplace. That’s what the Roman Empire was like, too; people strengthened their affiliations with it in order to do business.
Culturally and politically, to me this is the most essential and poignant part of the comparison between Rome and the US. It’s both deep-seated in its causes and far-reaching in its consequences.