M – to answer your question, I personally believe there are auxiliary psychosocial issues in American culture not directly related to firearms which contribute towards a culture that tends towards violence. This includes things like substance abuse, fatherlessness, and the glorification of gratuitous violence. I think if you study the trends of these factors you will find a correlation with violence. If you curb these trends you will also curb all forms of violence, including violence involving guns.
I don’t think an obligatory psychological evaluation for firearm purchases will prevent gun violence. This is because in order to prevent an individual psychologist from violating the rights of others, the test will have to be standardized and not subjective. Once it’s standardized, people can just learn to answer the questions correctly. Also, psychologists aren’t mind readers.
One thing you might find interesting is that license-to-carry holders in Texas are extremely less likely to commit a violent crime than those who are not licensed, and psychological evaluations are not a prerequisite for licensure here.