Training is twofold. Unfamiliarity is a serious problem, I believe you said that you're ex LEO, I went through OCS in the Marine Corps (dor'ed before you ask) and I've seen seen some really bad habits at civilian ranges, I'm sure you have too. I've also seen my redneck family members keep loaded weapons in the open around children. These people need some more training. Two, mandatory training would allow instructors to spot potential crimminals, crazies and terrorists and red flag them for further investigation. I used to train a lot of foreign pilots, (the 9-11 high jackers trained 10 miles up the road from my school). After 9-11, every instructor had to go through training to spot potential terrorists. It seems to have worked fairly well.
You're right that alone this won't reduce the murder and suicide rate, that's another issue which needs to be dealt with through community mental health and poverty reduction programs. Every gun owner should be lobbying Congress to implement more spending in these areas. However, having to qualify with a weapon would make you come into contact with more officials. That would potentially allow them to spot people who might be suicidal. My wife is a psychologist, the threshold for determining suicidality is fairly specific and simple.
Training would also reduce the murder rate because as you know, most crimminals are essentially lazy. Beyond your occasional psychopath, they're probably not going to jump through a bunch of hoops to get a gun.
Based on your responses, I don't know why we wouldn't allow someone like you to own an M-16. Especially used surplus built after 1986 that should cost $500 instead of $20,000.