Barring terrorist type attacks, and "mass shootings" aren't more people shot here in the US than in other first world countries? Would this number not go down dramatically if the civilian population didn't have access to firearms?
Murders will still happen, but without guns wouldn't the number be dramatically lower?
No, it would not. You are confusing *legal* access with access.
Most murders in this country are committed in urban areas with lower-than-average rates of legal gun ownership, largely by people with prior arrest records, many of whom cannot so much as
touch a gun legally. Chicago is Exhibit A on that point, where lawful ownership is well below average, and where around 90% of murderers and 50% of victims have prior arrest records. Most of those murders occur in pursuit of other criminal enterprise, and most of them get their guns the same way they get their drugs. Taking away the right of mentally competent adults with clean records to own a gun would not affect those murders in the slightest. Most states without dysfunctional urban cores (e.g. Vermont, where anyone can carry a concealed handgun without a license, and AR-15's and such are legal and common) have murder rates comparable to Europe; our murder problem is primarily an urban-dysfunction problem.
As to the efficacy of bans, did a Federal ban on alcohol stop people from drinking alcohol? No, it drove it underground, and thereby exempted alcohol from all taxes and regulations. It also pushed the market toward harder and more profitable forms of alcohol (away from beer, toward distilled high-proof forms) and vastly increased the social cost of alcohol consumption.
Has the 70+ year old Federal ban on cannabis stopped people from using cannabis? No, it drove it underground, and thereby exempted cannabis from taxation, distribution controls, and point-of-sale age limitations. It also pushed the market toward harder and more profitable drugs (cocaine, crack, methamphetamine, etc. etc.) and vastly increased the social cost of drug use.
Given those examples, why do you think that a Federal ban on gun ownership (which is laughably impossible, given that we already own 310+ million guns, tens of billions of rounds of ammunition, a billion magazines, and given that gun ownership has majority support among the public, law enforcement,
and military) would impair criminals from getting guns in the slightest? It would simply drive the production and distribution of guns underground, making it exempt from all regulation, and push the market toward submachineguns and ex-military automatic weapons. Cartels can and do manufacture guns from scratch, or obtain them through corrupt government/military/LE channels, and distribute them, and more dangerous types are far easier for a criminal enterprise to make or obtain than semiautos are. If a ban were to drive all gun production underground, then the U.S. gun scene would start to look a lot more like Mexico's, I suspect, as guns could be smuggled into the country disguised as routine cocaine shipments. So, no, that would not be a benefit.
As to lesser bans, such as banning "assault weapons" (i.e. civilian rifles with handgrips that stick out), more people are murdered annually using shoes and bare hands than are murdered using all rifles and shotguns combined. Twice as many are murdered with knives as with all rifles and shotguns combined. More people die in bicycle accidents than are murdered using rifles and shotguns combined. So how would a ban on some types of rifle handgrips affect gun murders at all?