To play the ultimate Devil’s Advocate, the Romans did leave a lasting cultural impact on Brittain. So in a way we have a cultural bloodline that is distantly connected to Rome.
The American system is a direct descendant of Enlightenment Classicism, which includes a respect for the Classical Republics. Athens, Rome, Thebes, etc.
American federal government and arguably as a result liberalism is quite literally an imitation and attempt at modernization of the Roman Republic, which is, among other things, why we adopted the eagle as a national symbol and have a fasces in the House of Representatives.
Yeah, there’s a fasces there. Symbol of Rome. It’s been there since before Mussolini claims he invented fascism