Really? So an assumption of guilt, and you have to prove you're innocent? You have to prove a negative? And who decides whether you can buy a gun or not? Your MD? A psychiatrist? Clergy? Neighbor? Family?
Tell me how you would actually execute this requirement. Then look at the causes of death in this country, and tell me why put the effort in gun control and ignore causes that are orders of magnitude greater than mass shootings. I mean, if the goal is really to save lives...
A mental health requirement has nothing to do with assumption of guilt or proving innocence, and such requirements exists for some types of jobs/licenses.
https://www.faa.gov/news/fact_sheets/news_story.cfm?newsId=20455:
"U.S. airline pilots must hold a Federal Aviation Administration (FAA) airman and medical certificate in order to fly.
....
How does an AME assess mental health?
The FAA medical application form includes questions pertaining to the mental health of the pilot. An AME may ask questions about psychological conditions as part of his/her assessment Pilots must disclose all existing physical and psychological conditions and medications or face significant fines if they are found to have falsified information. They must report any health professional visits during the previous three years. The AME will use this self-disclosure to ask additional questions about mental health issues. The AME can order additional psychological testing, or defer the application to the FAA Office of Aerospace Medicine if he or she is concerned that further evaluation is necessary.
Additionally, if the FAA receives information from another source that a pilot may have a mental health issue, the FAA's Office of Aerospace Medicine can direct the pilot to provide specific documentation and/or a psychiatric and psychological evaluation from a mental health care professional in order to make a determination about the pilot's suitability for certification.
If a pilot experiences an incident that appears medically related, the FAA will request additional medical information to determine the eligibility of the pilot to hold a medical certificate. If an FAA flight surgeon determines that a pilot with a valid medical certificate no longer meets the medical standards, the flight surgeon will then recommend that FAA counsel revoke or suspend the medical certificate.
Certain medical conditions such as a psychosis, bipolar disorder and severe personality disorder automatically disqualify a pilot from obtaining an FAA medical certificate and prohibit them from flying. However, many pilots have conditions that are treatable. Several U.S. airlines already have reporting and monitoring programs that provide the pilot with a path to report their condition, be treated for it, and return to the cockpit once the FAA has determined – through a rigorous evaluation – it is safe to do so. The FAA addresses the medical certificates of those pilots on a case-by-case basis.
The FAA does not release medical records on living pilots, including the results of any pilot’s medical testing, because medical information is covered by privacy laws. "
Edit: Fixed copying the wrong section of the linked article.