Yeah, but why would the Demogorgon have the slightest idea what a bear trap was, what it would do and how it would be triggered? To it, the bear trap was just a thing on the floor, just like it is for actual bears.
Well, my point was that not everything in the real world is reflected in the Upside Down, and there's no rhyme or reason for it. All the real-world trees are reflected when Nancy crosses over, but the fort in the woods has nothing around it. Joyce paints letters on the wall and Mike immediately sees them on the other side; what if she had drawn them on a sheet of paper instead, and then carried the paper from room to room? Why are there houses but no cars? If there is a plan, it might be something along the lines of: The Upside Down is a purely mental plane and doesn't really exist until someone observes it, and then only things that are significant to the observer are there.