Since we're at a point where many people are under-employed, and we expect many more to become so, we can probably re-institute something like this.
After all, the United States was a crazy experiment to revive 2,000-year-old Greek idea called 'Democracy'. While we did have slaves at the beginning, we have managed to enfranchise all adults politically. Maybe the Ecclesia could work, too.
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 administration of the colonies in the period leading up to the revolution.)
Insofar as the US (under the Constitution, at least) was an experiment in government, it wasn't in revive a dormant concept of "democracy", but in vigorously and fairly explicitly adopting the novel tripartite separation of powers model of Montesquieu.
> we have managed to enfranchise all adults politically.
No, we haven't. We have in principle (though less so in practice) eliminated certain bases of disenfranchisement, but it is not the case that the US has, at any point, enfranchised the entire adult population, even on theory, much less in fact.
Which church heirarchy? The secular heirarchy of the Catholic Church (which you seem to be referring to) certainly isn't an example (while there were certainly councils in which voting occurred, the members of those councils were not, for the most part, elected by the people below them, but appointed by those above.)
The monastic heirarchy perhaps had greater similarity to representative democracy, though I'd still say it was at best loosely similar to representative democracy rather than an example of it.
But that model is basically based on the English government with Parliament and a king in place of Congress and a president, isn't it? There was definitely a lot of neoclassical thinking among the Founding Fathers, although I'd say more inspired by the Roman Republic than by Greek democracy (to which the American system bears very little resemblance).
Anyway, curiously, a lot of early discourse uses "democrat" or "democracy" as a pejorative akin to "anarchist" or something.
I'm not a classical scholar, but I get the impression that later times preferentially transmitted the less democratic points of view. I.F. Stone also wrote about this in The Trial of Socrates.
Not really; the British system of the time was certainly an important influence on Montesquieu, but it didn't exhibit the three-way separation of powers between executive, legislative, and judicial that his model called for.
At the time Montesquieu was writing (there has been some practical evolution towards an independent judiciary since) Parliament held not only legislative power but also (in the House of Lords -- which at the time was also the dominant House in terms of the legislative function, though that is very much not true now) the judicial power as well.
Again, the then-current British system was one of the primary reference points which informed Montesquieu's model (and he clearly saw it as far superior to the French system of the time), but it wasn't designed around the three-way separation of powers with mutual checks and balances the way the US system under the Constitution was.
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.
Greece and the Roman Republic and Empire came to be seen as purer, grander and more refined past, which drove a lot of effort into re-discovering information about them, which led to an increased interest in archeology, and eventually to things like neoclassism.
Dictators and radicals alike looked for lessons, and found them in different places for centuries. E.g. the former have often had an extreme fascination with the idea of continuity with the Roman Empire (see one of Napoleons later extreme examples of trying to be Roman); the latter with the nascent democracy of the Greek city states and the Roman Republic.
You find it everywhere, not just in philosophy, architecture and art: English itself was subjected to a sustained "assault" of writers trying to bring more Latin and Greek words into common use.
A bit cheek-in-mouth: Everyone wanted to create the new Rome, ever since the fall of Rome (e.g. consider the Holy Roman Empire and the idea of "translatio imperii" which was used to justify a tenuous connection to the perceived glory of ROme ). They just disagreed (strongly) about what was great about Rome.
As to being a true successor, recall that the Holy Roman Empire was famously neither holy, nor Roman, nor an empire.
The "Byzantine Empire" is equally a misnomer. Constantine moved the capital of the Roman Empire to Byzantium-- renaming it "New Rome"--for defensive and commercial reasons. The Roman Empire itself remained. The notion that the "Byzantine Empire" was a successor to the Roman may arise from the fact that the eastern parts of the empire had always used Greek as the language of administration and as a lingua franca. Greek was barely known in the West from the fall of the eastern empire (ca. 476) to the Renaissance, when Greek scholars came to Italy as the eastern empire was contracting.
Given the Roman Empire's survival until 1453, the fall of Constantinople, a claim of succession is best made by the Russian Empire. Their Orthodox religion and Cyrillic alphabet were clearly derived from Greek Orthodoxy and the Greek alphabet.
Couple that with the invented principle of translatio imperii , and they glossed over the multiple long breaks in lineage, and lack of even an unbroken connection between the territories ruled.
There's the old joke about the HRE: It was neither Holy, Roman or an Empire - the emperor ruled on paper, but it had very limited practical effect other than letting a smaller and smaller set of families reflect in the glory of an Emperor title.
As an aside, that aphorism about the Holy Roman Empire is so well-known that it has the unfortunate trait of being spouted by people who know nothing else about the topic (not that I'm accusing you of that, if it sounds that way).
Call me old-fashioned but I don't think locking people in as a permanent underclass is a good idea.
And practically speaking I'm not sure how a slave society where the slaveholders have special rights to participate in democratic society is an improvement over a system where poor people have trouble participating because of their jobs or their resources but not because they don't have the right to.