Well, the thing is your suggestion explicitly infringes on second amendment rights of law abiding US citizens. You are talking about practically criminalizing the abnormal. Probably worse is that you're talking about publishing a list of the abnormal with wich to discriminate by. But, y'know, only a particular subset of the abnormal. That's okay.
There is no answer to be found in knee jerk single focus responses. This guy was depressed, lets limit the rights of all depressed people! This guy played video games, lets limit video games! This guy voted for the green party, lets outlaw non-republican or democratic voters!
Gorth pointed it out best. It's not just one thing. Many things contribute and it's improper to just pick and choose the aspects you think are okay to isolate. Violent media, healthcare, social problems, guns, and much else. Many of these are problems we already know about and work on. However, other people choose to play a blame / defensive-blame game that only serves to confuse the issues instead of look at them.
The two most important things I think should be done are better education systems in regards to making the public aware of topics of social problems, mental health, and violent media beyond the media arguments. And more responsive state and local governments that implement more trial measure laws with guaranteed expirations should they not show the desired effects.