Obviously, the best approach both in efficaciousness and from a perspective of liberty and diversity is to improve treatment access and eliminate barriers like stigma, miseducation, and psychological quackery like Scientology. We also need to pursue research to find better ways of treating or managing conditions like malignant narcissism, psychopathy, and so forth.
This goes beyond health care reform and PSAs. It means that schools have to teach about mental illness issues. It means that the average person has to be prepared to promote good information about mental illnesses and disabilities. We have to have a public support system that causes people who may have a mental illness to feel empowered to go get diagnosed, get treatment, and have the support and understanding of their families. Scholarships will have to be pushed through both by private and public actors to promote more therapists and social workers. And, while we're on the subject of social work, we need to fix our failing social work and foster care systems with actual money and reform.
Until we can do that, it seems grotesque to me to pursue approaches that are repressive or violate the civil liberties of the mentally ill.
A smaller aspect of this will have to be training for police, for reasons I will get into in-depth a little later. If police are better able to understand the mentally ill and defuse situations, that will massively reduce the number of times that the mentally ill actually do harm others. Most mentally ill people who do harm others (which, again, is a tiny minority) do so out of fear, paranoia, confusion, anger or frustration.
I am sure that there are other smart and creative policy approaches we can try at all sorts of levels, but to me the approaches centering on treatment access, reducing stigma, and empowering the mentally ill will be the best.
Avisia's point is utterly crucial, however. Everything from our natural fear of people who are different to procedural cop dramas have helped a lot of us to think that it is mostly the mentally ill who harm others. In fact, this is totally false. The vast majority of people who harm each other are not mentally ill, the mentally ill are tremendously likely to be victims, and the vast majority of the mentally ill will never commit any serious crime.
Still, there is a nugget of truth to the idea that the mentally ill can be dangerous. In a report debunking the "war on cops" myth, the FBI found that a lot of cases where officers got shot were due to the mentally ill. This is of course a very small phenomenon in general, since cops are actually safer on the job than ever.