You correctly state that if there were no guns, there would be less injury. The outcome equation is basic, and has been understood in law enforcement for decades if not centuries: Act = motive + method + opportunity. Limit people to a less efficient method, and you will reduce the scope and severity of the resulting acts.

Beyond the fact that this answer does not actually change the motive element of the equation - you haven't actually made a better society, you've just made one that has to make due with less effective methods of injury - there is the problem that Sean has often pointed out. In actual attempts to implement the model you propose, the results have been...well...equivocal at best. The Utopian problem comes into play: you ban the guns, but the guns that were there in the first place take decades to get weeded out of the system as the result of the active effort of the criminal element to retain them, with the further result that the effectiveness of your solution is questioned and you lose public support before your solution can reach its optimal effectiveness, and neighboring systems remain an illicit source of contamination so long as they do not follow your model.