Would police and army or similar organizations not have any psychiatric checks or tests before they are let loose with firearms(?). If so why not civilians(?).
They are not given exams because they are given weapons. They are given exams because they are given power, authority and huge amounts of responsibility. If these things are abused the organization could found liable. Carrying the weapon is merely a tool to help them carry out duties.
Purely an aside but not everywhere does mental health evaluations.