Some things cannot be effectively regulated in this manner. At all.
There is simply no way to stop people from building their own 3D printers. There are too many open source designs, and they can be built with very simple parts that are readily available at the hardware store. Most hobbyist-level 3D printers basically come as a kit that they have to assemble themselves anyways. What happens next? Background checks to buy stepper motors? Background checks to buy a microcontroller?
To me this is like trying to mandate government backdoors in encryption algorithms. There is literally nothing that would stop criminals from just using an open source encryption algorithm that doesn't have a backdoor, so you end up just making it so all legitimate communications are less secure than they should be.