I submit that we have a good and evil problem in the US much more so than a mental illness problem or a gun problem. We can certainly talk about solving mental illness and gun issues, but both of those existed long before our current problems.
Our leaders reflect our society and so they are not capable of dealing with evil and good because they do not think in those terms any longer nor do they have a common frame of reference for good or evil. We have been told for a couple of generations that we should remove objective standards of good in favor of total relativism, so now we are not capable of answering problems that primarily stem from evil.
C. S. Lewis saw this many years ago. He wrote in The Abolition of Man that a person’s head was the center of intellect and the belly the center of animal desires. What linked them was the chest, the part of us that discerns between our minds and our animal lusts. “We make men without chests and expect from them virtue and enterprise. We laugh at honor and are shocked to find traitors in our midst.”
I would build on that by adding: We remove an objective Good by which we can measure all people and are shocked to find murderers in our midst.
When the medieval cathedral of Notre Dame burned, some said that modern man is incapable of rebuilding it. Not because we cannot build buildings, but because we have lost the sense of the sacred. We wrongly think that bricks and mortar can rebuild a sacred space and wrongly think that removing weapons will remove evil men and that medical exams will diagnose evil intent.