Why are minifigure wrenches tapered at the end?
Your second guess was correct. It's not just a wrench. It's listed as a Screwdriver/spanner on Lego.com:



This part was also included in several sets in the Games line as a human tool to remove tiles from the dice. It's unclear (at least to me) whether this part was intended to be used for tile removal when it was introduced in 1979. Here's an example from the Creationary instructions: