in engineering, you test every proposed solution in as close to a real world situation as you can manage
we should reality-test the solutions from both sides of the fence:
1) “an armed society is a polite society” - fence off some state, like utah or someplace, posting a warning that everybody there is required to carry a firearm at all times. measure the change in the violence rate
2) establish another area where more restrictive gun regulations are enforced and measure the change in the violence rate there. of course, one could argue that such an experiment has already been underway for a while: it’s called “europe”