Yes, that should be a disqualifying factor.
There are certain things that severe mental health issues and defects preclude people from doing. Sounds "harsh" and unfair, but it's the reality.
If we swapped out the topic and made it about something other than guns, it would be very obvious how flawed your proposal is.
For pilots, the FAA defines following medical conditions as disqualifying:
- Angina pectoris
- Bipolar disease
- Cardiac valve replacement
- Coronary heart disease that has been treated or, if untreated, that has been symptomatic or clinically significant
- Diabetes mellitus requiring hypoglycemic medications
- Disturbance of consciousness without satisfactory explanation of cause
- Epilepsy
- Heart replacement
- Myocardial infarction
- Permanent cardiac pacemaker
- Personality disorder that is severe enough to have repeatedly manifested itself by overt acts
- Psychosis
- Substance abuse
- Substance dependence
- Transient loss of control of nervous system function(s) without satisfactory explanation of cause.
Should we lift those restrictions because it may discourage a person with any of the conditions above (who wants to fly a plane) from seeking help for their condition? Or are those restrictions there for good reason?