I use Slavery for almost the entire game.
1. It's a great way to deal with unhappiness. Just build something that requires 2 population. The first death removes the original angry citizen and the second death removes the new one generated by the whip.
2. It's the perfect way to deal with unhappy people in starving, recently-conquered cities. They're going to die anyway. Might as well die building a Theatre that will make the survivors happy ;^)
3. It's cheap and none of the other civics in this branch are particularly compelling. Who cares about worker speed? Build enough workers and this is totally irrelevant. That leaves caste system and emancipation, both of which are useful, even necessary, for specific strategies, but not necessary for my more generic "out-tech and out-maneuver" strategy. NOTE: I haven't played above Monarch, but up to that level I get by just fine with the never-ending slavery civic.... If caste system allowed unlimited engineers (in addition to scientists), I might lean more towards it. But as it stands, I usually find it more efficient to have huge cities with lots of worked tiles rather than specialists. Possession of the pyramids (with access to representation and its nice specialist beaker bonus) would obviously change that.
4. It gives great tactical flexibility. If you're in a building phase and suddenly someone decides you're just weak enough to pick a fight with, you can very quickly add combat troops to your queues, whip them, and be ready to fight. If you're in any other civic than slavery, you'll either need universal suffrage or a turn of anarchy. That doesn't help when the enemy is one turn away from attacking. And yes, there are plenty of other ways to deal with aggression, ranging from cash upgrades of obsolete units, through diplomacy, all the way to having enough units not to appear weak. But since slavery gives you the option and the opportunity cost is negligible, why not make use of it?