It is a minor part of the article, but I'm surprised they introduced it only to get it so wrong.
The U.S. Gun Control Act of 1968, among other things, requires traceable serial codes on guns, something that has become a key element of forensic ballistics. In some circles, this is seen as controversial, as highlighted by a case involving “ghost guns” that the Supreme Court is hearing this session.
First of all, serial numbers don't have much to do with forensic ballistics. Generally, in forensics, investigators are comparing items in their actual possession -- shell casings, bullet fragments, and weapons recovered from the scene of a crime or from a suspect. Serial numbers don't help with that.
Serial numbers are useful in investigating gun trafficking -- it's actually very similar to the example of car theft that the author presents early in the article.
Regarding the "this is seen as controversial", that is a claim that is absurd beyond belief. What is at issue in the case is when the requirement to serialize adheres and to what it adheres. That is a complex issue. A gun is made of dozens of components. Many are tiny with small surface areas, like springs and pins, and many are replaced over the life of a gun, so serializing them would (a) be ineffective and impractical and (b) could actually confuse the identity of the gun.
So when do we serialize and what do we have to serialize? For a long time, the settled practice in the industry has been that there is one component that is "the firearm". This part generally is large, is subject to low mechanical stresses, and can be expected to last the life of the gun. This is generally a part called the "receiver" or "frame".
If the receiver is ever damaged beyond repair, regardless of the state of the other parts, then a "new" firearm has to be created and serialized. Although the barrel, trigger, &c, are all the same, it is a different gun now.
This system has actually worked pretty well and has allowed for relatively robust tracing of stolen guns and guns found in investigations of international arms trafficking.
Collections of parts that make up an incomplete gun are of two kinds -- if the receiver is in that collection, the collection of parts is a firearm and has to be sold according to the rules governing transfer of a firearm; if not, it isn't.
A receiver or frame starts life as a large block of metal or plastic. So what if we sell people a parts kit where we have every part of the gun except the receiver, and also an appropriately sized block of metal or plastic? Nothing in this combination has to be serialized and it is not a firearm.
Until recently, this was not really an area of much activity because, while a receiver is subject to low mechanical stresses, that is in relative terms -- relative to other parts of the gun. It is nevertheless a component that takes a fair amount of machining and finishing to get made. What brings us to the "ghost guns" discussion and the Supreme Court case linked in the article, is the degree to which home manufacturing with light tools has improved in recent years. It is actually possible now to make a pretty good receiver without a machine shop. Some people came up with a business of selling people almost complete guns, with a block of plastic or metal and some jigs that allowed them to readily complete the receiver. This is an edge case and it will take some thought to establish when, exactly, we apply the rules regarding serialization. The people making blocks of plastic probably will not be required to serialize all blocks of plastic simply because they are potential firearms (along with potentially being many other things); but the people buying the blocks of plastic to put into kits that they then sell to others in order to make guns probably will be seen to have created a "constructive firearm" and so will be required to serialize them.