I didn't say you couldn't. My point is, that the puzzles were put in the game to present a challenge to the player, and enhance overall game play. They weren't really intended to be scrutinized on the level you have taken it to.
And my point, was that the Villagers aren't presented as the erectors of these artifacts, but rather as the restorers of them.

Would you say that the teams of archeologists who uncovered Stonehenge, and started it's reconstruction, imbue the same significance on it that the original clans who erected it did?

I seriously doubt that's the case. Indeed, we can only speculate on the original purpose of it. My point is that the Villagers don't "construct" these things, but rather reconstruct them. They may "honor" the idol, "relax" in the garden etc but they do so in a state of marvel more than one of religion.