Tombs
I think there are two distinct sets of areas to place traps. The first is tombs and graves. Places that hold the dead. The easiest justification for having traps here is religion. The builders believe that at some point in the future the bodies need to be taken away.
This is likely to be combined with some mummification process, either Egyptian or Incan. It might even be bog mummies. Now, why do they need to be taken away? Maybe a savior will come that lets all the dead rise and join him on a journey. The savior will be smart enough to solve the puzzle and mere mortal plunderers will be blocked.
Alternatively, maybe the puzzles aren't really puzzles, but a mere test for the spirits/souls of the dead. They would see through them with ease. Again, it's us mortals that need to stay out, while still allowing the spirit to reclaim his body at the right time.
Cities
This is harder to justify. Entrances to settlements can be guarded with fake or hidden paths against outsiders visiting. I'm not sure those or a maze would count as a puzzle.
Again, religion can be used. Maybe their religion foretells a great end of the world that starts with all of the chosen people dying. But maybe the buildings are shielded against spirits. Lined with salt, herbs or runes, to keep the evil spirits in the dark outside.
But now the souls of our chosen ones are trapped inside. Maybe they need guides, valkyries, to take them to the afterlife. Perhaps the intricate locks are made for such divine creatures. Simple mortals and ghosts struggle but, divine beings can easily open them.
A completely different approach: maybe they weren't build as puzzles. Their society build a very extensive network of pullies and levers. Opening doors, trapdoors for supplies, adjusting machinery. Now over time things broke. Instead of a well working system it became a broken death trap.
Perhaps the system doesn't rely on inorganic cogs and ropes. Maybe it's organic and without caretakers it grew, made connections it shouldn't. Maybe the switch for the door now also open the airlock. A broken one that's now filled with poisonous gas instead of the supposed medical herbs. Again a death trap.