Geographic distribution of voting power is not an essential component of Republicanism. Although unequal voting power was a feature of traditional Roman Republicanism, that distribution was a hereditary distribution, not a geographic distribution.
More to the point, the US system is so different from the patrician/pleb system of Rome that calling our system Republican while calling (our system minus geographic distribution) not Republican is a pretty freaking arbitrary line in the sand.
Also, it's worth noting that Cicero's greatest effect on Roman politics was foiling a somewhat Haysian rebellion.
> I'm not sure why you brought up that most people arguing about something tend to pick the side that benefits them. I live in New York City. This does not benefit me.
I won't presume to know your political beliefs, but it's worth noting that you could increase the power of your preferred coalition while weakening your own vote.