Summary

As per the documentation Board administration, you can create new status through the board's column settings on certain circumstances:

Project must be currently using the Simplified Workflow.

You need to be a Jira admin or board admin (to view the board configuration). In addition, you need to be a project admin for the one project that is on the board.

Still, it might be difficult for admins to check all different settings involved to determine if a user is supposed to have such permission or not, specially when it comes to big sites with a big user base.

Suggestions

As a means to reduce the effort and stress on admins to monitor and properly manage that permission, make it more clear in the UI when a user has the permission to add statuses or not.

Example: the button Add status could always be displayed but be either enabled or disabled if the current user has or does not have the necessary permissions. At the same time hovering over the button would show a tool tip to explain why the permission is disabled or not (e.g. user has/doesn't have permissions A, B, and C).