These exports are already illegal under US law, but it is deliberately made difficult to enforce ultimately because the gun manufacturers love it when someone comes in every week and buys 50 rifles without concern for price and then drives them off over the border. They’ve managed to convince a lot of legal gun owners that the rather straightforward steps that would be necessary to prevent this from happening are a major infringement on their rights and preparation for some kind of government purge.
A very similar situation existed in Florida with the “pain management clinics” that were selling massive quantities of drugs while the government did nothing about it for years.
Taking apart a gun is not a legal loophole, all guns have one piece, the frame/receiver, which is engraved with the serial number and in the US is legally considered to be “the gun”, as opposed to “parts”.
Being a “straw buyer”, e.g. buying gun on someone else’s behalf, is illegal in and of itself even within the country. To legally export firearms, parts, or ammunition outside the country requires a license from the ATF. This is not a trivial license to get, and needs to identify who is ultimately going to receive them.
Right now about 600 guns a day cross the border into Mexico, but they are not going legally.