If the law required that everyone carry a gun with them at all times what you'd soon discover is that people would begin shooting each other, for a wide variety of reasons. Sort of like it is now.
If, on the other hand, the law required each person be accompanied by an armed robot which could sense when its charge was in mortal danger from another person, and would subsequently dispatch the danger, quickly and acurately, you'd find that the general populace would begin minding its manners, and shooting deaths would drop to almost nothing as only the suicidal would risk such certain doom.
What this means is that that average American is, by and large, thick as Alaskan honey and should never have access to something as deadly as a gun.
So the only trade-off for universal security is a vast army of deadly, armed robots with its own moral code. What could possibly go wrong?