To be more focused, I really don't think any of this addresses the "criminal element" very well. Most of the mass shootings have been by people who weren't criminals beforehand (though they were often being treated for mental health issues). If someone wants to reduce access to weaponry to that kind of person, its going to take a combination of gun use/storage regulations and a comprehensive "universal healthcare" of mental health programs.
That's amusing to me because it means anti-tax folks (who are heavily overlapped with gun owners) will have to cough up taxes for it. And gosh, if its such a good idea for mental health, why not for physical health given the incoming train wreck to the economy due to epidemic chronic health failures from a lack of preventative care available?