Ummm, as an Australian, I must say that I'm a bit offended by your remark about all 'democratic' nations being Republics

! Please stop being so US-centric.
As it happens, most European nations (and NZ) represent what the main difference between a 'Democracy' and a 'Republic' is. First of all, even where the nation HAS a President, AT ALL, that president is largely a figurehead with almost NO real power. Most, if not ALL, of the power in a Democracy is invested in either a Unicameral or Bicameral parliament. In a Republic, OTOH, almost all decisions made by Congress and/or the Senate are vetted/vetoed by the President IIRC. The President of a Republic is also the 'Commander in Chief' of that nations defence forces AND almost single handedly elects the judges to the highest court. In a 'democracy', these roles and decisions are spread out over many more people, with no one individual having sole authority! Another point is that all 'Democracies' have a Prime Minister, who is the nominal 'head' of the governing party(s)-though this person is the most visible part of the government of the day, they are only as powerful as what his/her cabinet will allow! A governing party or even opposition can cast out its leader at any time! How 'Democratic' a democracy is really depends on what country you look at. Most European nations use a 'Mixed Member Proportional' system, where the composition of parliament fairly accurately represents the voting intentions of the public. In Australia and the US, however, we only have two parties that can have more than 1 or 2 members in either House-courtesy of the 'Two-Party Preferred' system-which leads to a kind of 'Duopoly' arrangement of 1 Government-1 Opposition party.
Anyway, I admit that in the modern day Republics and Democracies might not LOOK very different but, at a fundamental level, they are in fact VERY different, so I feel that both examples should remain in the game. To better define things, though, we do need a combination of Modern and Classical examples of these two government types PLUS we need Social Engineering traits so that the player can better define what his government looks like. For instance, the 'Republic' in a Civ game might SOUND democratic and free, but when you look at the SE settings, you realise that both 'Sufferage' and 'Libertarianism' are set below 50% (or below 10 on a 1-20 scale), meaning that this is more of a 'Banana Republic', a fact which may well be further reinforced by a look at that civs economy and military

!
Anyway, hope this explains things a little better!
Yours,
Aussie_Lurker.