So, if you go to a NES shoot, you only shoot the gun you carry? I doubt it. I wouldn't as long as someone was willing to let me shoot their hardware.
As for training, I went into a trafficking stash house once. We ended up with a couple pistols (1911 knockoffs and a 357 revolver) and a SKS type rifle/pistol/monstrosity with an attached magazine (stock sawed off haphazardly). I was the only one that had any idea how to clear/safe the weapon. I happen to own an AK, which is similar to a certain extent. It was the only weapon in the house that wasn't loaded ready to go. So, yeah, ATF guys, you know, the guys who deal almost exclusively with illegal firearms, should know how to handle almost any firearm. That training is continuing, because if you haven't handled a gun in a while you forget how it works.
As for the agency existing, I'd tend to agree it's one of those that should go away or at a minimum be swept into another 3 letter agency. HSI suddenly had an interest in the deal I was a part of, ATF tried to swing by but HSI yelled 'claimed' and took over the case.