What would suggest we do to prevent people who shouldn't be armed from being able to get a gun?
The system to stop that is actually already in place. Part of the problem is the lack of communication between departments. All too often after an incident we hear later on that this person or that person was under investigation but somehow city or county officials weren't aware of it and the person ended up slipping through the cracks.
Another part of the problem is some states still have racist based laws in place that go back to Jim Crow era. NY is a shall serve state meaning that they use their own discretion to allow for a person to get a firearm. That was used to prohibit black ppl from buying firearms for years on top of years.
The current system needs an overhaul and that starts with acknowledging that they've dropped the ball too many times. Federal, state, city and county need to be on the same page so that no person is able to go in for a purchase where a flag doesn't go off if something isn't right about that person. The question is whether the government will ever admit these shortcomings and make the necessary changes.