An interesting question with a simple answer. Perhaps an answer few want to hear in an era where everyone seems enamored with excessively complicated weapon systems. The shotgun is for deploying the maximum amount of force possible to destroy as much of the adversary as possible in the shortest time frame possible.
It is, compared to the rifle, a close range weapon. Some will begin to raise a finger in objection, but what they intend to show as a weakness is actually an asset in the sorts of fights a weapon like this is best for. Use a shotgun against a rifle in a rifle problem the rifle will always win. But put a rifle against a shotgun in a fight that utilizes the shotgun's attributes and the rifle will lose.
The shotgun is not good for shooting people at long distances, nor is it a high sustained fire weapon. Close range, high likelihood of hitting even when the speed of the fight exceeds the users ability to deploy traditional marksmanship principles, high likelihood of destroying/killing the intended target with few rounds fired, fast into action from inaction (exceeded only by the pistol), and simple manual of arms that requires minimal maintenance. Those are the attributes of the weapon and its utility is in urban confrontations inside of fifty yards where pistols are usually encountered.
Detractors will attempt to show the rifle's superiority here by running drills on steel or paper and counting the score on a target. With this weapon don't think of a score...think of killing a target. One press of the trigger with any other weapon yields one projectile. With the shotgun one press of the trigger could yield as many as 34 projectiles delivered en masse at the close range target. Thus even a peripheral hit could be fight ender for the bad guy.
The shotgun does not benefit from detachable box magazines that the rifle-minded enginers have tried to bring to market. Yes it is interesting and I suspect they will sell plenty to those who go about with completely unloaded shotguns who suddenly feel a tactical need to be fully loaded. Other than that, the detachable box magazine offers no advantage in a shotgun gunfight.
The shotgun does not benefit from high capacity magazines. And by that I mean more than five to seven rounds. Shotgun gunfights are not long drawn out infantry-like events with fire and maneuver and mag dumps. They start suddenly and, just like pistol fights, are over quickly as well. The damage the shotgun does insures this. There are those that want to argue about this point. I will point out that shotgun ammo has a higher weight factor and that the more you add to the weapon, the heavier that weapon becomes. And a heavier weapon is slower to use. So by making a shotgun heavier you are actually making it less useful . You are making the shotgun less useful by adding ammunition that you will not use in the fight.
The shotgun does not benefit from addition of accessories. I see shotguns sometimes with so many things added that they have lost all utility in a fight due to its clumsiness and weight. Shell carriers on both sides, detachable magazines, lights and lasers, overly bulky design. Some things are meant to be sold and possessed, but only those who collect such things will ever use them, and then only on the range in a contrived shooting drill to emphasize that weapon's utility...usually a drill that has no bearing on reality. We have seem weapons like that...the HK Mk 23, the Taurus Judge, the pistol bayonet, and drum fed shotguns (and other derivatives of the theme).
What does the shotgun benefit from? Very simple. The shotgun benefits from things that enhance its utility in its given mission. Shorter is better within reason. Lighter is better without compromising other factors. At least 5 rounds. As a point of note I personally have used shotguns in gunfights many times. Most rounds ever fired? Four. A sighting system that is useful beyond ts sporting application. I like rifle slug sights...I like red dots. If the weapon sees any use in low light, a small modern lightweight light attached.
That's it. The rest is up to the user and his skill with the weapon. I don't care what the Remington reps say, or what the Mossberg reps say, and specially I do not care what the hell kind of shotgun the IDF wanted for Christmas. Study the reality of the fight and organize your weapons accordingly without concerns for fashion. Then develop your skills with the weapon and you will find the properly organized shotgun is just as deadly today as it was in the past.