I think America's issue pertains more to the frequency of serial gun shootings, the use of guns to kill family members by design or accident, and the ability for young children to be able to access guns and ammo with tragic consequences. Those are the casualties of a thriving gun culture society.
At this point you would think simple things like enforcing safe storage and gun ownership registries would be focal points to at least avoid simple tragedies and so law enforcement can track guns for crime prevention purposes.
As for the frequency of shootings...Ive found evidence that supports your position and undercuts it. So, I figure they are stable.
Killing family members by design....you cant legislate away the crazy. Meaning, nuts are always gonna find a way. I remember after SandyHook some uninformed person said to me,"If only we didnt have guns, those children would be alive". To which I said,"um..no. Lanza couldve called in a bomb threat or a fire, and simply drove over the kids with a stolen school bus". Crazy will find a way.
Killing family members by accident...this is solved by education and training. Ive been around guns my entire life..never had an accident. The only accidents I have ever heard of were by people f'n around with a gun.
Children gaining access can be addressed in several ways..education(again), safety lessons, and just keeping guns locked up when not in your immediate possession if you have young kids around(age to be determined by the parent who knows their own kid).
Safe storage is a great idea. I have a big safe and a small safe. Laws that make it mandatory to have a safe are burdensome to people who cant afford them. Guns can be made inaccessible with a lock attached to it...cheaper alternative. Either way, a law mandating "safe storage" can and will be used as a club by a zealous prosecutor when simple child-endangerment laws would suffice.
Gun ownership registries...I am going to guess you probably dont own a gun. The only thing a registry does is make it easier for the "Government" to one day take them away, since they already know who has what. Every dictator started with registration of firearms. Dont think it can happen here? Ask gun owners in NY,NJ and CA...and NewOrleans during Katrina. Besides, a registration of gun owners and their guns doesnt prevent crime. How could it?