Speer and the Nazis did make a lot of use of industrial Slave Labor towards the end of WWII - see Tooze's Wages of Destruction book on the German economy under Hitler, but it also emphasized the negative aspects of slavery: the wastage was huge, efficiency per person was abysmal, and they had to constantly keep adding more Slaves because the workers died by the thousands - one of the reasons why Speer spent 20 years in prison after the war.
Slavery is really 'efficient' only in Special Circumstances: work that is so dangerous no one will voluntarily do it, like in the poisonous silver mines of Laurion in Greece or the underground factories of WWII Germany, or in malarial areas of Central and South America where white European workers died faster than they could be shipped in in early Colonial times. The 'cotton slavery' of the American South worked temporarily because it had a labor-intensive crop (cotton) which was a money crop as long as textile factories would take any amount you could raise and pay well for it, but it came with major security costs (the white South was already an armed camp before the Civil War) and, like slavery in Classical Era, depressed innovation since 'labor saving' was not an issue and nobody in charge of the work force had any vested interest in changing work conditions to make them more efficient.
Sooner or later, ALL slaves Revolt, from Spartacus to Nat Turner. The Social Aspects of Slavery are actually Cultural and Innovative Negatives, because society and innovation (science) are both depressed by slave or slave-like conditions. If we are going to have Slavery in a game, and if the game is really going to be based on History and not Fantasy it's pretty near unavoidable, then you have to do it Right: show the negative aspects with the positive, and the fact that the negative aspects get more and more dangerous as the game goes on. Eventually the 'slave society' winds up like the Confederacy, with lots of slaves, lots of cotton, but only one cannon foundry, a couple of iron works and not a single manufactory to even make uniforms for their troops - who have to put down several rebellions against the slave owners even while they are trying to fight off a massively better equipped opponent.