Tbf "mentally ill" means a lot more than "a danger to themselves or others." We already do block those who have proven themselves a danger (or we can if the cops do their goddamn jobs which is often the point of failure for cases like Cruz from Parkland), it's one of the rules we "don't" have that if you have been involuntarily committed or convicted of a particular crime(s) you're barred from ownership, but should we ban someone from a right simply for having ADHD, autism, bipolar, gender dysphoria, etc? All that'd do is discourage therapy and be discriminatory, and it's wrong.

Where I live, in EU, guns are legal but regulated. Long guns, including semi auto assault rifles require a hunting license, which includes what's called a psychotechnical exam, a basic health, sight, hearing and basic psychological exam. Short guns require an actual psy exam, 30-45 min.

At least it weeds out clear mental health issues.