As a retired detective, I believe that I am qualified to shed some light on this question of shotgun evidence. For the most part, the vast majority of crimes are solved with informants. The telephone is the one most valuable asset in investigations that police don't talk about as it takes away the "magic" of finding a perp. It is what they don't talk about even on the television shows. Now, back to your question, the shell casing, if found, can be utilized as evidence once someone has called in and snitched out the perp. Otherwise, it is impossible to inspect every shotgun owned or borrowed by known perps in the area with a history of violence. After those known to have a grudge against the victim are eliminated, it ain't magic that hauls the perp to jail. It is that unknown call that connects the cops with the actual perp. The wadding is usually found but is of no use except to identify the manufacturer of the ammo. It is normally found in the victims body and is partially mutilated. How many people in a square mile area use Remington, Federal, or Winchester ammo? There has to be that one factor that is not talked about-the snitch. Once the perp is known, a variety of ways can be found to eventually get to the evidence. These methods won't be told to the media. In other words, a warrant can be issued for other reasons and served at his home and the gun seized as a search incident to arrest. Then a match can be made with the casing. All legal, case solved, and it makes for good "forensic science".
Let's take a similar example. A house is broken into and items are taken. Fingerprints are found, good latent prints. However, the perp has never been printed before as is common with so-called "first offenders". Since no matches are on file, what next? Maybe he left a piece of his shirt caught on the window he broke along with blood. None of it is worth a cent without someone to match it up with. Criminals might be smart in crime but they always tell their friends, always. Bragging rights. They can't help it. Using false ID to pawn the items eliminates a good lead. We still aren't anywhere. Now--a good cop develops a good team of informants. Very little came down in my area that I didn't know about. I cashed in a few chips and got the info I needed. Then developed the case. In my career I never lost a case in court and I worked a lot of felonies in my time. I gave a lot of breaks to those perps that deserved them and got everlasting loyalty from them. I could get on the phone and call my snitch in the area of a crime and get the identity. Then I would go to the DA and we would explore how we could legally deal with the situation. Since we had no evidence except the word of a heresay informant, we had to explore other legal ways to obtain the evidence. It always worked. These snitches are the backbone of a good police department. The telephone is the best piece of laboratory equipment ever.
Remember, most policeman are commited on crimes that they can observe. They like to ride around waiting for something to happen. But when it comes to good, hard detective work, just put out the word among your snitches and wait for the phone to ring. Almost every dept has a snitch fund that can be used to pay for good info, but I never had to use it.
After the conviction, you will see the news about great police work along with how the forensic labs and profilers solved the crime. In real life, that ain't what happens. Yes, the labs and profilers and all this other high tech stuff is used to cement the case, but the starting point has to come with someone on the street that knows who did it and confidentially makes that magic phone call.