There are two main reasons to enable the Status feature:
If Status is disabled, you lose the ability to use a competency’s status to separate “draft” or “in progress” competencies from “live” ones that users are actively working on. However, you can use the competency setting “Make competency and its children visible to users who can be evaluated” and the learning objective setting "Ready for Evaluation” to achieve similar effects.
If competencies are typically created within a single course offering, user enrollment and course start and end dates can also be used to prevent users from accessing competencies before they are finished. Also, if competencies are typically created within a single course offering by one person, you might not have any use for the workflow functionality that comes with status.
However, if competencies are created and tracked at a higher org level (perhaps they are organization-wide) and shared across multiple course offerings, if users work toward them gradually over time, and especially if you have a formal workflow process surrounding the competency life-cycle that involves multiple users, then you could benefit from using status.