A gun-free zone is not such a good idea, much like an encryption-free zone would be, or an alcohol-free zone (the latter has been tried).
I would rather go for Swiss-stye mandatory gun training, and keeping a gun in (almost) every home. But, like the Swiss, I would require not just storing the gun in a certified safe box, but also providing an ID + a proof of mental sanity, and registering the gun. That would raise a much larger wave of protest though, both from the "left" and the "right". Even though, IMHO, it's the only sane way.
I have never lived in a country where people are allowed to keep guns. That scares the crap out of me.
Not just because of random strangers. I went through a mental health crisis, and there was a dark time where if I had had a gun I would be dead now. No amount of lockers or safe boxes or mental health tests would have saved me from that gun.
And wtf do you need a gun for anyway? I have never, not once, been in a situation where having a gun would have improved it. Why do you think giving everyone guns would be a good thing?