One mechanic I'd love to see added to Civ is disease. It's had huge significance throughout history and would be another fun layer to the game.

For example, if you settled near a swamp there would randomly be disease outbreaks. When you encounter a new civ your diseases would have a chance to infect each other's units, and you would spread it to your Civ if you brought them back.

Military units who are fortified in certain terrain would slowly lose health as they suffer from things, and you could have civilian units that can undo disease damage. Hell, you could purposely send infected units to an uncontacted civs and decimate their populations.

To fight this they could add a hospital district, new great people, and new technologies.