My early life and work has carried me to areas of high crime, most of those crimes being gun violence. I've known quite well many offenders. I still visit two of them in state pens here in the midwest. Trying to count all that I have known who have used guns illegally it looks to be about 78 or 79 over a period of the fifty some years of my 74 years being alive.
I carry a gun everywhere I go that is legal to do so. No. Not because I fear those people. The reasons I carry have a lot less to do with those people than with the ordinary people who drink and lose it, smoke and lose it, see a tailgater in their mirror and lose it, etc ad infinitum. I'm a calm person by nature, and even more calm when I carry as I adhere to principles brought out in my MP military training and much more recently in my Concealed Carry Permit class here in Nebraska. I, like almost all responsible gun carriers, react kindly to perceived slights or traffic potential hassles; it would take a true life and death situation by another person for me to even think of my gun out there.
"Mental illness" is a HUGE net that covers almost every human on Earth at some point in their lives, and some for most of their lives. It's not a perfect indicator of who should have access to firearms (or sharp objects, or hammers, or eye drops). Background checks help a bit with those who have already drawn attention to themselves by committing domestic violence or other violet crimes. Those checks can fail, of course, due to overlload and time requirements on the FBI and other involved agencies.
Is there any course of action that could stem gun violence in the U.S.? In some countries it's about disallowing firearms to various degrees, some even not allowed at all. And some countries with little to no restrictions have very low gun crime, such as some Scandinavian countries. For us it has to be education. I feel that the NRA has it right when it comes to that. I part company with them, though, on their scorched Earth approach to fending off all gun laws, that's just crazy. We obviously need gun laws. But we have to be clever.
I think it's very much about culture and how the country was born. Here in the U.S. it was about violent revolution, and several violent domestic wars over the past two and a half centuries (think it has been just the Revolutionary War and then the Civil War? Nope:
https://en.wikipedia.org/wiki/List_of_conflicts_in_the_United_States).Guns are a big part of what shaped us and it has been often and it has been engrained in our being as Americans.
I like the approach of permitted concealed carry, with classes, but I feel those classes should be longer and with more teaching on the responsibilities and mindset of a gun carrier. I also think that those same classes should be required
for the purchase of guns, not just for carry.