I used to do a similar thing in Sins of a Solar Empire, but in Civ5 I usually find by the time I've killed the last Civ I'm badly wanting to start a new game (I enjoy exploring new maps), but maybe I'll give it a try (I usually play marathon/huge maps though).
Not OCD the game is called Civilization after all and having a Civ you can be proud of seems a reasonable goal.
Not OCD the game is called Civilization after all and having a Civ you can be proud of seems a reasonable goal.