I understand the intent, but feel that there are so many other loopholes that put much worse weapons on the street than a printer. Besides, my prints can barely sustain normal use, much less a bullet being fired from them. I would think that this is more of a risk to the person holding the gun than who it's pointing at.
All states require you to get a background check on the purchase of a firearm from a gun store. Waiting periods are in a minority of states. Pretty much any felony, even nonviolent ones prohibits you from buying a gun.
The 'gun show loophole' is actually just the in private party sales (like selling your neighbor your gun) no background check is mandated. This is because the law requiring background checks is a federal law and the federal government has the authority to regulate interstate commerce but not intrastate commerce. Some states like NY have stricter background check laws than the federal law.
Bows, knives, & machetes all don't require background checks. Grenades, technically any can get a license to own & make explosives but each one carries a $200 tax in addition to the hoops required to get the license, so pretty much no one really does that recreationally.
I didn't mention it in my comment but you assume a lot of risk in a private party sale. We aren't talking about illegal guns but ones that have been registered at some point in time if they aren't historical.
If you want to sell a gun, you should go through an FFL to avoid liability.