Quite often it’s more annoying - they omit details that would spoil the plot. Do most criminals think of wiping fingerprints off the bullets? How come we never hear from the taxi driver who took the perp to the scene? Where did that cellphone come from (speaking of tracking serial numbers)? The world is full of minute details, many of which appear contradictory.
Yeah, we need more of that.
Don’t harass law abiding gun owners, but keep the guns out of the hands of criminals.
Dogs, cats & cars are registered so why not guns?
A serial number is also good for the manufacturer and gunsmiths. Generally speaking, you’ll know what year a firearm was manufactured based on the serial number. And if you know this particular model of pistols made between 2004-2007 has a common defect you can put out a recall, it makes diagnosing problems easier, etc., etc.
The idea of finding a gun at a crime scene is a Hollywood plot fantasy.
Just about every commercially available mechanical/electrical/electro-mechanical device has a serial number. And there’s a reason for it, naturally.

The term “ghost gun” is a lot like the term “assault weapon” used in modern politics. It’s an intentional misnomer designed to make something sound scary. Most “ghost guns” are not really ghost guns in the way that the term is being tossed around today. They are mostly guns made for legal use by law abiding individuals. They are rarely used to commit crimes and are rarely used to subvert gun tracking laws. There have been cases where someone who isn’t allowed to own a weapon (felony conviction or whatever) and has been caught with a “ghost gun”, but the vast majority of unserialized non-NFA guns were legally made and have not been used for criminal purposes.
For the past 2.5 months, I’ve been serving on a grand jury for one of the counties bordering Chicago. About 30% of the indictments we hand out are for felons with firearms on their person. Most of these are conventionally purchased guns that made their way to the felon by one means or another (the Taurus brand 9mm seems particularly popular with felons in my area). But an alarming number are the “ghost guns” that you indicate are “rarely used to subvert gun tracking laws.” At least one or two cases per week.
Not being a gun guy, I had never heard of “ghost guns” before starting on the grand jury.

Just about every commercially available mechanical/electrical/electro-mechanical device has a serial number. And there’s a reason for it, naturally.
Wine has serial numbers. Using the bar code on a wine label, plus lots of databases, you can track the contents to the vineyards the grapes came from, where the cork came from, and plenty of other things.
I found this out when I was on a task force for the computer company I worked for looking at traceability. It was embarrassing that vintners did better with a $20 bottle of wine than we did with our servers that sold for hundreds of thousands of bucks.
Serial ids are built into microprocessors also. I’ve used them to track down the root causes of problems.
For guns, it would be useful for manufacturers to be able to trace the origin of guns that blew up in their owners’ faces and do a recall. I don’t know if that has ever happened, but I could see it as possible.
It also allows the owning organisation to track possession and assign responsibility in case of loss.
Territory of Dakota
Fort A. Lincoln
Before me, 1st Lieut. J.E. Porter 7th Cavalry, Judge Advocate, General Court Martial, personally appeared Corporal George W. Wylie, Company “D” 7th Cavalry, who being duly sworn according to law deposes and says:
That on the 1st day of November 1875 he was ordered out with his company during an alarm of Indians, and in the gallop from Fort A. Lincoln to the Big Heart River his pistol, an improved Colt’s revolver, Cal.45, No.5637, the property of the United States, and for which Captain Thomas B. Weir, 7th Cavalry, is responsible, was lost from his belt holster [Old pattern Remington belt holster], and that the loss was occasioned by no carelessness on his part.
That upon his return to the fort he reported the loss. And that all due and diligent search was made for the pistol and that it could not be found.
Deponent further says that Captain T.B. Weir, 7th U.S. Cavalry, is in no way responsible for the loss.
[signed]
George W. Wylie
Corporal Co. “D” 7th Cavalry
In the US, the 1968 GCA started requiring serial numbers, before that many (most?) manufacturers still put them on. They serve important roles in quality control (was a certain run of serials poor quality), inventory for the manufacturer, diagnostics for users (certain serial runs are more valuable, or give information about year of production). Some surplus rifles from other countries may or may not have a serial, but importers will add their own, so sometimes there’s two completely different serials.
How does the court define “ghost gun.” There seems to be a lack of definition, both in the news and even legally.
Taurus is a Brazilian brand that is considered mediocre at best. There’s definitely crappier brands out there (anything considered a “Saturday Night Special”) but their quality control is considered poor, and if you do need repairs the CS is not great.
@DrDeth that’s already a mega-felony.
It is quite rare.
Once in a a while a careful search will find the gun dumped in trash, etc.
They found a gun in the subway station where the Brooklyn shooting happened today, but I don’t know if it was the gun the shooter used.

How does the court define “ghost gun.” There seems to be a lack of definition, both in the news and even legally.
How you define it is in itself is an issue. The receiver for some gun designs can literally be a hunk of channel stock. If you haven’t punched holes into the channel stock to attach the other bits, is a hunk of metal channel stock a receiver? At what point does it become a receiver?
You have to be careful how you define an unfinished receiver, otherwise every hunk of metal C-channel at your local Home Depot becomes a unregistered firearm receiver.
What Biden is specifically going after in this case are what are called 80% receivers. This is also a term that is poorly defined, but basically refers to a receiver that is not finished and is technically still just a hunk of metal, at least from a legal point of view. It’s not necessarily that 80% of the work is done, they just aren’t finished to the point of being a functional receiver (which is why "80% receiver is a bit of a misnomer). These have become very popular in recent years.
An 80% receiver for an AR-15 is a very specifically shaped hunk of metal. It’s a lot more complex than a hunk of C-channel from Home Depot, but it is literally just a hunk of metal.
But that’s not true of all gun designs. Many gun receivers are not complex at all. You can make a slam fire shotgun using just a couple sections of pipe. In the 1990s, a British guy named Philip Luty who was very opposed to gun control published a very simple sub-machine gun design that you can make using only parts that are available at your local hardware store (recently someone actually made one according to his plans, apparently it’s a rather crap gun and very uncomfortable to shoot, but it does work).

I cannot imagine a scenario where a hard-boiled detective would bust a murder case wide open based on a serial number.
Certainly this could happen. Imagine the purpose of a VIN with your car, and the registration of you with this number.
Right. Just to follow up. A “gun” must be purchased (commercially) through a licensed firearms dealer with a criminal background checks. “Gun parts” can be purchased by anyone online. So if a trigger spring is broken, I don’t need a background check, I go to one of the many places online that sells it.
The question immediately arises: What is to stop me from buying every part of a gun and just building a complete one with no background check? The answer is that the law typically defines the “gun” itself (firearm in the law) as the receiver, the place that accepts the ammunition, called the lower receiver on an AR-15 type rifle.
So if I only want to buy an AR-15 lower receiver, it must be serialized and I need a background check, even though, as said, it cannot fire and is typically a hunk of metal.
From my understanding, and it is hard to get accurate information given the politics of the issue, technology has improved such that a person can manufacture enough of the lower receiver (dubbed an 80% receiver) to make home construction of the remainder of it very easy, if you listen to gun control proponents, or very very hard, if you listen to gun rights activists.
But, it is still not a lower receiver as defined by law, and needs no background check or serial number. So the policy question is whether these should be regulated like receivers or left largely unregulated like gun parts.

Once in a a while a careful search will find the gun dumped in trash, etc.
It seems they often catch the shooter with the gun.
Doesn’t help to solve the murder case, but can help to track down the source of the gun, assuming the shooter did not purchase it legally.
Why would they do that?
To catch straw purchasers, or other individuals selling guns to prohibited people.
Surely there is a legal distinction between merely making a gun (which, if you have the skills and equipment, you can make from scratch just like the original factory—not sure what you mean by “technology has improved” but use a 6-axis CNC mill if you want), and selling guns, which requires serial numbers on your products. My tube of toothpaste has a Lot # and I am pretty sure it is legally required to be there, too.