Are you actually suggesting eliminating all guns wouldnt make a society safer?
You could make society safer if you eliminate all objects from the peoples' access that throw things at high rates of speed. That means no slingshots for kids, no archery for anyone, no model rockets, etc. They're all too dangerous.
You could make society safer if you force all vehicles to travel less than 35 mph. We lose roughly as many lives on the highways every year as we do to guns, yet I see everyone perfectly willing to accept those deaths purely so they can drive fast.
You could make society safer if you eliminate all sharp objects and the means to make dull ones sharp. Knives kill a lot of people every year and they are too dangerous to leave in the hands of free people.
You could make society safer if you eliminate all chemicals that cause death when ingested. Poison kills people, and they need to be controlled.
You could make society safer if you eliminate all chemicals that can be mixed and go bang. Park a truck in front of a building, hit the ignite switch, and people die. How better to stop it than eliminate fertilizer?
So, yes, in your extreme, ludicrously unworkable, theoretical utopia, no guns at all means a "safer" society, but it also means a far less FREE society, and remember, even in the strictest, most utopian of all "gun free" societies, there are still two groups of people who have and use guns. If you don't know who, I'll tell you, but you should be able figure it out.
I am also seriously stating several things regarding trying to eliminate guns in America:
1. You will never get rid of all of them because there are far too many of them and far too many owners see no positive benefit to getting rid of them. Combine that with American independence, and you have a recipe where it becomes a game to own and hide guns, just like distilling moonshine and outrunning the police in fast cars became a game that ultimately turned into NASCAR.
2. Guns are not the cause of the deaths we see, and taking guns away will not remove the psychoses that are driving people to kill other people, it will just cause them to turn to other methods of achieving the same ends.
3. 3D printers can now make gun components that are untraceable. Sure, they can only be used a few times, but they can still kill people. Good luck trying to shut that down.
Freedom is dangerous, messy, and chaotic. It's also preferable to the alternative. And finally, remember that those who trade freedom for an illusion of safety wind up with neither.