I learned more about safe weapons handling in hunter safety class in the 9th grade, and from my father before that, than I got in Basic in 1970. It's all about "muzzle awareness", and got more training in that from the Michigan State Police, and not the Army.
Part of this problem is that 95% of the troops in the Army will never fire a round outside of the rifle range. Another part of the problem is that the Army spends more time on sensitivity training than safe weapons handling. The USAF is even worse, they aren't even issuing empty weapons to their troops in camp. And ammunition production was basically stopped for several years during the klinton regime, so only the lucky troops got a couple of rounds per year to fire. No firing, no safety training, either.
I have a few suggestions, which I know will be ignored. First, instant court martial for anyone having a negligent discharge, even if you're a general. Second, take away the rifles from all the REMFs and paper pushers, and give them a stainless steel DAO five-shot .38 snubbie. Hell, give one to EVERY troop, and get rid of those damn Berrettas. The elite troops would also get a modern sidearm in 45ACP.
Training on a double-action-only revolver is simple, unless you're a real retard, and shouldn't be in the military in the first place. The object is not to hit a target at 300 meters, but three. The revolver is considered always loaded, and there is no external safety. It's always ready to fire, and everyone knows it. With stainless steel, daily maintenance would be "unload it, blow away all the dust, and reload".
Personally, I'd rather have five shots with a .38 than an empty M16 that I have to lug everywhere, drop, lose, and abuse. And as a real infantryman, having a last-ditch holdout weapon would bring an extra comfort level.