The New York Police Department has reportedly seen a 60% increase in ghost guns seized from city streets for the past two consecutive years. NYPD recently traced some online ghost gun sales to a “ghost gun printing operation” filled with 3D printers and firearms nestled within a daycare center.
I have no idea from this if the increase in ghost guns was attributable to 3D printing, or if the increase even represents a significant number.
It also seems like this would be really difficult to enforce. You can buy hardware or kits to build your own printer, or you can buy an old printer off someone else.
All that said, if it represents a reasonable concern and they figure out a way where it's not trivially circumvented (both of which seem unlikely), I really couldn't care less about a background check.