Earlier quoted context omitted.
> After all, the United States was a crazy experiment to revive 2,000-year-old Greek idea called 'Democracy'. Not really. Representative democracy as the substantive form of government was an established tradition in Britain and it's North American colonies long before the US (a prime motivation for the revolution was perceived increasing deviation from that norm by the central government in respect to the administra…
While obviously informed by modern thinking, the Founders rooted the American experiment firmly in classical Greek and Roman tradition. There's a reason why US government buildings all look like classical temples.
It's not quite that simple. The US Federal style adapted neoclassist architecture from Europe, where Greek and Roman inspired revivals started in the mid 18th century when new archeological expeditions as well as artists bringing back impressions of Italy and Greece produced an influx of images and artefacts that made Greek and Roman architecture better known.
French revolutionary architecture went to a similar extreme as the US Federal style, and I'm sure it wasn't all a one way thing, and you're sort-of right in that certainly people were looking to the Roman Republic and the Greek city states as an ideal, and that was part of the fascination with Greece and Roman culture.
And the architecture in return did get an image tied to radicalism and republicanism as a result of the extent of its use in the US and France after the revolution (the French then went on to take it to the extreme, when under Napoleon the French Empire style tried to do everything bigger, shiner and even more Roman).
But the Greek and Roman revival didn't start in the US, and often copied then-modern European architecture rather than copying the originals.
An example where we know the direct influence is the layout of Washington D.C. - Jefferson provided l'Enfant with maps and sketches of a number of European cities to use as inspiration, with Karlsruhe being one of them.
Karlsruhe had been built from scratch starting in the 18th century, following a strict planned layout with a palace at the centre, radiating artery roads out from the palace gardens, aligned with the wings of the palace, and was a major force in spreading the influence of strict geometric city plans that used the shape and regularity to draw attention to important buildings or monuments as well as to tie the city together. Washington D.C. (and many later US cities) certainly in turn influenced further city plans in Europe.