You cannot buy a New-In-Box (NIB) firearm from your neighbor, unless he/she/it is a Class 01 Federal Firearms Licensee...and that is definitely contrary to the Constitution (IMHO).
I accept the need for FFLs, because I don't some psychotic on leave from the local Home for the Bewildered buying a .50 Barret, and having to fill out the yellow form at my local FFL-licensed dealer helps prevent that even if just a little, because the dealer isn't going to put his license and business on the line for one sale to a weirdo.
So because someone might do something illegal or crazy, you want to restrict everyone's right to do that thing? That is what is known as "prior restraint" and has repeatedly been ruled unconstitutional in the 1st Amendment context. It is the equivalent of banning automobiles and liquor because some irresponsible bartender **may** give another drink to someone who's obviously drunk already, and that drunk **might** go out on the road and kill someone. Sorry, that doesn't wash with me. You could make the same argument for lots of household chemicals, but no one has because it would cause too much inconvenience. Same for gasoline - remember the Happy Land Social Club massacre in NYC in 1990? 87 people died because one sick guy bought some gasoline and misused it.
By the way, psychos and criminals can get guns pretty much anywhere - restricting access and availability only restricts the sane and law-abiding.