You're off base with how good you think slavery is. It's not only possible to win deity without slavery, but I was ignorant of the mechanic when I first started beating deity. (Granted I relied on like chopping praets and stuff). And since you asked for a forum game example.... I get to share mine ^^
https://forums.civfanatics.com/threads/k-mod-deity-quick-writeup.511322/
It's Deity, quick speed, K-Mod, and I didn't use slavery. Not a self-imposed restriction, I didn't think slavery was useful.
The popularity of slavery is somewhat tied to settings. For a standard pangaea normal speed game on deity it's pretty essential. This a game where you need to rush to gain every possible city spot you can, and you frequently fight early wars. Both those things are what typically necessitate slavery, provided you have some food.
But change the game to quick speed and slavery becomes much less effective. Slavery converts food to hammers, but in an isolated game it's all about commerce - I'm focusing everything on spamming villages or rushing specialists. I will also not get slavery if there's no food, as it's useless then. Most games there's adequate food (since you are picking your city spots after all), but I used to prefer masochistic maps, and usually those had poor food situation.
Slavery is also typically an obvious pick just because of the way civics work. It competes against a default that does nothing. It's the first civic available, and its opportunity cost is 1 turn of anarchy and like 1 gold in maintenance. The 1 turn of anarchy isn't nothing though. Most civics you can plan ahead and pair up such that you can swap 2 civics for 1 turn of anarchy but not that first slavery pick. It competes directly with Caste - arguably the most powerful civic in the game, and slavery gets more inefficient over time as city sizes increase and hammer costs increase. Eventually you swap into caste, though when you switch depends on your personal play style and your reliance on great people.
Slavery competes with:
- Early: 1 turn of anarchy / medium vs low upkeep. Usually slavery worth it.
- Mid: Caste system. Depends on how important specialists are, whether you want to run more specialists than you're currently able to, and how many cities need those free artists for quick border pops.
- Late: Workshops, powered by Chemistry, Caste + State Property. Workshops are just better at this point imo.
- Very Late: Happiness pressure may or may not force a switch to emancipation, regardless of whether you were running slavery or caste.
This seems perfectly reasonable. It's one of the more balanced civic trees.... as compared to legal which as was mentioned is pretty dominated by bureaucracy. Slavery can be incredibly powerful, but it's also the most difficult to use. Also makes sense.
The things that are actually brokenly OP in this game are AP or culture victories, and nuclear weapons. Though I even hesitate to say nukes are broken. They're certainly OP on deity, but this game was designed with more than just that setting in mind. Nukes aren't OP on say, Monarch.
It's incredibly hard to win on deity completely peacefully, at least for me, and that's regardless of slavery. Humans are much better at fighting wars than the AI and that's a huge advantage to just give away. Also, it's virtually impossible to compete with the AI's commerce output in the modern era if you're not bigger than them. Only time I've out-rexed the AI peacefully is in favorable water maps where I can settle islands / choke points faster than the AI and go from there.