1. No military alliances or trade embargoes. How are you going to ally against an enemy when they all have the same name? On the other hand, Rights of Passage agreements and Mutual Protection Pacts are still possible.
2. No slave workers. How are you possibly going to make them slaves when captured workers are of the same nationality as you?
3. Culture flips like mad. Every city will have Zulu people who admire one particular Zulu culture, but whose?
4. Impi on Impi action. When was the last time you triggered two golden ages on the same turn?
5. Ahh, and here's the kicker. We want to cure our schizophrenia somehow. Desired victory condition: Diplomatic. Guess what? You can't vote for yourself, because you don't know which Shaka is you!