No,...that`s not it at all. And unarmed population coupled with armed criminals means less guns but more violence, I guarantee it, Look at other countries, bad guys with guns rule citizens without guns.
This is a very American centric view. I can tell from the "bad guys with guns" sentiment, as if there are easily boxable groups of "good guys" and "bad guys".
I grew up in the states, but now live in Iceland, a nation with zero gun crime. We finally had a single time the police had to shoot a person, and not only did they apologize for the necessity afterward, but offered counseling to all involved and it was in the national news.
Now I don't think just gun control laws alone will fix America's problems with gun violence, to do that would require reopening the Reagan shuttered mental institutions, fixing America's abysmal social mobility and slave wages, and many more areas that would improve everyone's quality of life (happy people largely don't risk their stable lives to commit crimes), but we can see just from the areas of America that enforce existing laws, gun violence is lessened.
After living stateside for 25 years on the east coast, west coast, and middle, and now Iceland, I can absolutely say I feel safer with fewer guns. (rifles are allowed, hand guns are not. Not even the police are armed, but we do have a special swat team that can be called who does have guns). Safety comes from a working society where everyone feels they have a place and a way to contribute and get ahead, not a violent murder stick.
here are some handy links:
Gun ownership positively correlated with homicide rate
International study concludes gun ownership positively correlated with homicide and suicide rates
The more lax a state's gun laws are, the more gun crime occurs in that state
Decreasing guns on the street by better enforcement of existing gun control laws = less crime
Castle doctrine laws increase homicide rates
Guns in the home more likely to be used stupidly than in self-defence