Regarding this mad focus on health care...
For one, people are talking about it as though the US is abnormal in this regard. I'm pretty sure that NO country has easy, socialized access to mental health care. Universal health care provides basic (life or death, infections, broken bones... things like that) care to the public. Mental health is not included. In fact, psychiatrists and the like are generally viewed more positively in the US than in most countries. There is LESS of a stigma against it in the US.
Second of all (and perhaps more importantly), even if it WAS public, nobody can force someone to seek psychiatric help against their will, and 99% of these types of psycho and sociopaths won't seek help no matter what. Perhaps it could be identified in children, but once they reach adult age, they're adults and that's the end. Furthermore, there are a a shitload of awful parents out there - many with unwanted children - who could/would never identify something like this in their child... and there are even more parents who would never be able to admit it to a point of taking their kid to get help.
While mental health care definitely should be improved, it is not the answer here. Regulating and limiting guns is the answer.