I'd just like to add to this
Huge Map, no mods, all game modes (except Tech Shuffle), 12 players, 18 city states (30 player slots) - Free Cities exist.
Huge Map, no mods, all game modes (except Tech Shuffle), 18 players, 0 city states (18 player slots) - Free Cities exist.
Huge Map, no mods, all game modes (except Tech Shuffle), 18 players, 18 city states (36 player slots) - No Free Cities exist.
Huge Map, no mods, all game modes (except Tech Shuffle), 18 players, 12 city states (36 player slots) - No Free Cities exist.
Huge Map, no mods, all game modes (except Tech Shuffle), 12 players, 24 city states (36 player slots) - Free Cities exist.
Huge Map, no mods, all game modes (except Tech Shuffle), 13 players, 24 city states (37 player slots) - Free Cities exist.
Huge Map, no mods, all game modes (except Tech Shuffle), 14 players, 24 city states (38 player slots) - Free Cities exist.
15 players however will break Free Cities... this is a very confusing bug.