This won't work. Gun restrictionists just want to ban guns. They aren't actually concerned with safety, and thus they don't care if you are trustworthy.
This would detract from their effort to ban guns. Getting to root cause is not really part of the agenda. Note that any new focus placed on mental health, under the auspices of dealing with one of the root causes of violence perpetrated using firearms, has been perverted into new avenues for denying law-abiding citizens legal access to firearms.
I doubt either is more effective, since most of the bad guys off themselves when they're done doing what they do. But I would prefer to see the second one.
We protect our banks , courthouses, federal buildings, politicians, their children, ... Hell , we protect guys digging a hole in the street - with armed men.
When the SHTF these are our adversaries. This makes me happy as I could probably handle a couple dozen myself as most will be running for their lives. we should make some DUMB FREE ZONE signs