I think that it's probably too late for the USA to regulate either firearms ownership or those with mental problems. The brutal fact is that there are way too many guns and unidentifiable troubled people out there.
The statement that 'it's not the guns, but the bad people that use them' is correct, but how much better would it be if society made a concerted effort to at least try and prevent weapons falling into the wrong hands? It wouldn't be a complete answer but it could reduce the size of the problem. At present the best people can hope for is to try to contain outbreaks of violence and clear up until the next time. My heart goes out to the victims and families.
I'm not anti-firearm, and speak as a lifelong shooter.