could there perhaps be an iron fist trait for older generals who have spent a very long time governing a city or with huge amounts of influence (obviously they would also need to be corrupt, have a position in government, selfish, possibly the presence of one of the despotic buildings like execution squares or gladiatorial arenas). They would be able to make lots of profit off of the city and avoid the suspicious eyes of those higher up thanks to bribery, making it unlikelyto be censured. obviously their methods of tax collecting and enforcing law would include torture, imprisonment, and "vanishing" political enemies. This might bring a law bonus at first, as well as decreased population growth (representing people being arrested/executed) but soon a second trait could arrive representing how tired the people get of such tyranny. this would cause severe unrest due to unnhappiness, less order due to law, and a decrease in personal security. Maybe their bodyguards might even become less loyal because they've been ordered to do comit too many crimes. it would be easy to look the other way as their leader is hacked to pieces. If possible you could make them likely to die earlier. it would be fun to see that they died from "natural causes" later on.

another suggestion, a general might lose some command/influence if they relied too much on mercenaries and not enough on native troops. as well there could be an "enjoys foreign culture" or "foreign wife" trait which might give them less influence and less command because his people no longer trust him. at least they would be less likely to get a powerful position in government. there could be a problem with determining what the culture of the general was, but maybe faction-specific buildings might effect this. ie: a roman who spends too much time in settlements with greek buildings might get the "wants to be greek" trait. When this general entered a roman settlement with a romans only building, he would get a trait such as "seen as a traitor" this would last only until he left and went to a city with a greek building, where it would cause the trait "feels right at home"

maybe you could also do this with schools and other cultural buildings. an intelligent general with the trait "philosophically inclined" might start to feel impatient in a city without an educational building. this could lead to all kinds of bad things like "sees others as inferior". The same could be done in reverse.

oh, just one other thing could perhaps be an "idealist" who could try to take away things like gladiatorial fights or high taxes. If they did implement high taxes, they would be merciful and also work harder to benefit the people. eventually their reforms in the city could lead to population growth and incredible loyalty. they could crack down on corruption and get discounts. Also, the people would be willing to work and fight harder and/or for less pay, since this man was so kind. at the same time, their security might go down when the local aristocracy feels like they've been wronged. on the other hand the people would be so loyal that no one would be able to attack this general. Obviously they would be hard to bribe, and unlikely to be a good military leader, since their morals would contradict military action.