Why is Rome important here? I can see the symmetry between Rome and what USA currently has - different rich powerful groups arguing and ignoring half the people, for example; rife corruption and nepotism - but how is Rome a model for a democracy, and one that seeks (in theory) not to divide the people into ruling and subservient classes at that?

I think part of the point is that aspects beyond democracy are taken for granted. The US citizenship and model of "being Roman" is pretty imperial in many ways. It has undersung virtues of tolerance. It doesn't matter if you were Greek, Gaul, Barbarian, or even Carthigian - once a citizen you are fundamentally Roman. Viewing nationality as not an immutable accident of birth is pretty damn "Roman". Many "modern" issues like Political Correctness and Multiculturalism are millenia old and can really be better described as "Imperial" Issues. They are encountered due to past and present expansionism and and broad interactions. Despite the negative connotations not everything classified as Imperialism is bad - just as it is a mistake to ignore the travesties of empires so is it a mistake to ignore its virtues.

Rome had many periods and the dynamics have played out before and provided disturbingly apt precedents even with the alien trappings and values.

Because the U.S. isn't a democracy it's one that was explicitly founded on the model of the Roman Republic, albeit one with a written constitution.

The rights to life, liberty, and the pursuit of happiness, for all (per Tho.Jefferson) seems pretty democratic?

Was the founders intention to have a super-class who had political determination?

Could you expand a little on your point?

Can you expand on this?

There is a school of thought (with some validity, though I think it lacks nuance) that points out that the early Roman Empire, the Principate of Augustus until the Dominate of Diocletian, tried to empower the Senate. The Senate had its set of provinces, the emperor his. The cursus honorum was still used to track and groom administrators and leaders and the senate's support (balanced against the army and the people of the city of Rome generally) still legitimized the emperor. But over time, goes this line of thinking, senatorial attention and interest fell away somewhat from administrative and managerial responsibilities and turned more into a social/politicking club, and the emperor "naturally" picked up the slack.

There is an element of bias to this, and it often reveals a political preference of the author, but it's not without some merit.

I believe the claim is that the Roman emperors came about because the Roman senate became so mired in infighting that it was incapable of governing. I'm not a historian, but from what I understand, there is at least an element of truth in the claim.

For a detailed version of this argument, I recommend Edward J. Watts' Mortal Republic: https://www.goodreads.com/book/show/39088591-mortal-republic

I was being a bit glib, and others have expanded better than I can on the theory (plus Roman politics is complicated) but here's an example of the theory: https://www.history.com/news/rome-republic-augustus-dictator