Does anyone really believe the more guns in circulation makes everyone in the country safer?
Yes, some people rational believe that.
More guns does seem to increase certain risks (improper use, accidents, suicides, guns getting into hands of wrong people) but reduces risks in other situations (self defense, civil unrest, government led genocide . . . which does thankfully sounds very far fetched but it happened in Europe only 80 years ago . . .and think about how Ukraine would be faring today if there were no access to weapons). I think it's embedded in the constitution to address these latter types of risks.
Personally, I think more constraints over gun violence portrayed in entertainment/media would reduce the risks too, but that would constrain first amendment rights (and constraining those is more conducive for other problems, including higher levels of corruption).
This is a challenging and important problem to discuss, but the complexities need to be appreciated.