I'm a pretty fit guy, but I'm sure the recoil of a gun could break my wrist (well, maybe a desert eagle, I was pretty good with a kalshnikov on my military trainig). I spend more time typing on a keyboard than on a shooting range (which is kind of expected, i'm a programmer). I doubt you can apply such logic as a large scale solution. Do we begin introducing shooting classes in high school, to protect all our citizens?

As for your bet - the paradigm would shift from bullying all people to bullying frail people and avoid rednecks, as far as the violent cops go. This would hardly solve the problem.