Early on in the game, whenever I capture settlements, I enslave them. But later on when I'm out in the British isles and stuff, I just begin exterminating for two reasons:
"Republicans who did not play the patronage game were ridiculed as the Mugwumps for sitting on the fence--their "mugs" on one side of the fence and "wumps" on the other. Historians generally consider this era a low point in American politics."--United States History by John J. Newman and John M. Schmalbach
1. The city may revolt (especially large ones) and not only break my line of territory, but also be filled with a huge army of gladiators and rebel heavy units. Not fun to fight and a waste of men who would otherwise be used in a garrison or for future combat. If the enemy faction is still alive, then guess what? They just regained their city after you wasted 500 men seizing it and won hundreds of free units to defend it.
2. Extermination brings much more denarii. A decent city will bring you some 10,000 from looting alone! Big ones can get you 20,000 or more. Often loot like that is the only thing keeping my gains in the positive after recruitment and construction fees.
"Republicans who did not play the patronage game were ridiculed as the Mugwumps for sitting on the fence--their "mugs" on one side of the fence and "wumps" on the other. Historians generally consider this era a low point in American politics."--United States History by John J. Newman and John M. Schmalbach