If you're nutty in the head, no gun for you. Criteria would have to be by a mental health professional (preferably MD), and could be appealed, but what percentage of these gunman doing massacres aren't fuckin' nuts? 0%?
If you discount sane workers driven mad, such as the streak of people, "going postal," you will basically be left with 0.
Have any of them done it and family/friends been like "Wow, he was just a normal happy guy, great dad, never any issues, everybody liked him."...not really, most are "yeah, he was batshit insane, I'm not surprised by this".
And, it seems a substantial portion have had some kind of treatment for their ills, too, so the MDs are there, and the records are there. Some will always manage to slip through the cracks, but when there is that obvious history, why weren't we doing anything? In many cases, because nobody was allowed to but the patient, and the patient is allowed to do whatever until he kills people.
Do note that there has been a little beneficial work going on. Virginia closed the loophole that made it so easy for the Virginia Tech shooter to get his firearms, as an example. A small step, but at least it's the right kind of thing to do.
But, there's even more reason to make it easier to remove such people's rights, at least on a non-permanent basis
(yes, there's more polite wording, but if you've got a problem with it, that'll be it, so there you go). Most of these people are not going on rampages, but may still be dangerous to themselves and others, and cause significant stress for their families, as they try to force them to get care because they care about them
(as opposed to trying to hide their craziness). Google is your friend, and I'm lazy, but mental health treatment advocacy groups are out there, and easy to Google for, with plenty of their own stats, suggestions, criticisms, and anecdotes.
Why don't we exploit the recent tragedies to prevent future ones, and also prevent the smaller-scale ones you don't read about every day? Seems to me like a much better way to make use of it than banning comfortable grips
(I can't even think of a silly scary thing about pistol grips, really), light hiking/camping-friendly stocks
(oh, I mean, "scary military-style tactical stocks"), hearing preservation equipment
(we all know a suppressor makes a 308 sound like a bouncing tennis ball, after all), magazines of decent size
(well, that'll be good for aftermarket magazine manufacturers, I guess), etc., to no meaningful result.