My home area had local option, home rule prohibition of alcohol until 1968, when sale of hot beer was allowed.
By the time I was seventeen, I could name seven bootlegging joints, which sold beer and booze, plus pot, pills, pistols and porn and served as meeting places for gambling and prostitution.
There was a cab company working with one of the bootleggers and you could call and have "passenger" Johnny Walker or Jack Daniels delivered to your doorstep (of course you had to pay the cab fare).
I am cynical about restrictions on legal markets in goods preventing criminal abuse of those goods, whether guns, alcohol, you name it.
As far as more restrictions on legal sales causing a black market in guns, hey we have a black market in guns.
The Bureau of Justice Statistics asked a sample of state inmates where they got their guns:
13.9% Retail Sources:
8.3% Retail store
3.8% Pawnshop
1.0% Flea market
0.7% Gun show
39.6% Friends or family:
12.8% Purchase or trade
18.5% Rent or borrow
8.3% Other
39.2% Street/illegal source:
9.9% Theft or burglary
20.8% Drug dealer/street
8.4% Fence/black market
The "retail sources" often involve friend, family or lover with clean record making the purchase. On friends and family supplying their guns to criminals, the NIJ "Armed and Considered Dangerous" survey of felons noted "friends" supplying guns to felons were often fellow criminals, as would be many family of felons. Now, would friends or family of a known criminal run a background check on their criminal family member or friend, and refuse the sale, trade, rent or loan if the check came back "prohibited person"?
Also in the "Armed and Considered Dangerous" survey 40% of armed felons stole guns, but only about 12% stole for their personal use: many stole for resale. Sources stolen from included:
37% stole from stores,
15% from police,
16% from truck shipments,
8% from manufacturers.
Leaves about 21% from individuals (cars, homes, etc).