We have universal background checks now for any new gun purchase. Other limiting factors are in place on a state-by-state basis. Bad people still get them.
If you are advocating for a more-stringent system where a person must in some way prove their worthiness in order to purchase a gun...be careful and ask yourself: Who watches the watchmen? Whoever enforces limits on guns will have the power to abuse those without guns.
That is the reason the US Constitution (AKA: our protocol for playing nicely with each other) uses the specific language to say that you are born with the right to have a gun and others must prove you to be unworthy in order to take it away.
If you produce an immutable blockchain for gun registry and licensing that no government or entity can abuse, co-opt, or manipulate...I might then be convinced of some of the viability of what you are arguing.
RE: Reality Check: Trump Did Not Make It Easier for Severely Mentally Ill People To Buy Guns