Quite honestly, as someone who became a Civilization fan at Civilization IV, and someone who uses many mods, the main, and actually only, reason I did not go backwards in history and buy Civilization I, II, and III is exactly because they don't use civics. Frankly, the civics in Civilization IV even felt dull to me. Mods like Rise of Mankind and its A new Dawn, however, did exactly what I want for the civics system. Governmental systems aren't just Democratic, autocratic, and socialist. The United States was never a Democracy until FDR. It was, before then, a Republic -- and some even argue against it. Some argue that it was Federalist, and the Federal government should therefore not have the same authority as that of a government of a Republic, as John Locke defined it. All these nuances aren't just minuscule. They are considerable and define your nation's identity. Just because countries call themselves the "Republic of Sudan" or the "People's Republic of China" does not mean they are just a Republic or a People's Republic.
There is more that goes into societies than that. What if they're a Republic that emphasizes State Property? What if they're a Constitutional Monarchy that controls the elected officials through a shadow government? All these nuances should be emphasized in the game, because I am sure that the silent majority fanatics of this game want the game to imitate politics as much as possible. I do like the idea that countries should be drawn towards certain civics, but it shouldn't be because of the country in and of itself. People need to remember that America in real life is not the same as the America in the game. An America that was founded in 4000 BC would not be the same as the one in real life. The countries in the game should be drawn to specific civilizations in the basis of its context, its history in the game. If a country just achieved independence from a monarchy, it might very well levitate towards a Republic. Of course, resources and whatnot would play a role as well. I've heard that Civilization V will be doing things with a Civic Tree or something, and it'd be interesting to see how it'll turn out. In terms of the current civics system, however, I think that something like this would grab the essence the government of a country.
ORGANIZATION: Federalism, Centrism, Confederacy
GOVERNMENT: Anarchy, Aristocracy, Authoritarianism, Autocracy, Consociationalism, Demarchy, Democracy, Fascism, Gerontocracy, Kratocracy, Kritocracy, Magocracy, Minarchism, Monarchy, Noocracy, Ochlocracy, Oligarchy, Panarchism, Plutocracy, Technocracy, Theocracy, Timocracy, Tribal
SOCIETY: Libertarian, Meritocracy, Egalitarianism
ECONOMICS: Capitalism, Subsidized Capitalism, Corporatism, Progressive, Socialism, Communism
RELIGION: Storytelling, Prophets, State Church, Intolerance, Secular, Atheist.
NATIONAL IDENTITY: Illuminati, Progressive, Free Trade with World, Patriotism, Nationalism, Tribal.
MILITARY: Feudalism, Standing Army, Volunteer Army, Conscripted Army, Unmanned Army.
Obviously, there could be more, but I think the above would be a step in the right direction. People play Civilization to make their own society. They want at least certain control over things.