Yes, we would. But how would we manage to do that? Banning guns leaves the law abiding citizen with no means of self defense, and the same way people manage to obtain drugs, belligerent people are going to obtain firearms via illegal processes.
So, we need to identify the leading causes of shootings and gun deaths, (not the gun, the mental part) and try to limit those. Also, perhaps passing a law that all gun owners must be registered with an up to date medical record of mental issues.