The subject line and main text of your question are slightly different. To answer your headline question, yes, such debates are happening. But the issue is sufficiently politicized by now that scientific analysis will be accepted by many if it fits the preconceived notions, rejected if not.
Some argue that "guns don't kill people, bad people kill people." What that means is that killers rather than gun laws are blamed, without necessarily questioning the mental health of the killers. Becoming a criminal is seen as a personal lifestyle choice of the criminal, who deserves the consequences if he or she is caught.
Others decry that the mental health system has been slashed to the bone along with other social services, and that police and the criminal justice system are used as an insufficient substitute.
The main text of your question is "pushing" for the conclusion favored by just one side of the debate. Many believe that it is the right position, but that is a political position, too.