Curiosity is a key trait for business analysts. This is especially true for contract business analysts that go from project to project.
At the start of any project, the business analyst must learn the domain. The business analysts needs to understand the domain at a detailed level allowing them to make recommendations on the best processes and the best way for applications to automate those processes.
Without curiosity, it becomes difficult to keep digging until you understand all the idiosyncracies amount the domain.
With curiosity, you are driven to find the nuances and how to use the nuances within the business processes and applications to maximize the value for the client.