Deaths from firearms, whether homicides or suicides, would be reduced were they banned.
According to the ATF, only 10-15% of guns used by criminals are stolen. The rest are legally registered guns, although they may have been transferred illegally or acquired with false affidavits and documents.
A black market in guns would be nothing like the black market in alcohol during Prohibition or that in drugs now. It's much harder and more expensive to smuggle guns than alcohol or drugs.
Prohibition didn't work because it was too unpopular, and it was easy for organized crime to bribe politicians and cops to look the other way.
Drugs are easy to produce, transport, and smuggle, and pot is immensely popular.
Arms manufacturing is not something done on a farm or with a still. And were guns to be banned I doubt that all those law-abiding former gun owners would go to the great expense and risk a prison term to acquire one on the black market.
I might have said that it'd be okay for single-shot weapons to be legal. But now that I know that more gun deaths are by suicides than any other cause, why make it easy for people to kill themselves?