I came across this, Don’t Dump the Pump Shotgun and saw a lot of the same folk-wisdom surrounding shotguns regurgitated again.

Why should you keep your shotgun in addition to your new M4 or other patrol rifle? It’s an intimidating and powerful weapon, that’s why. The presence of a 12-gauge shotgun and its gaping maw of a barrel can stop a bad guy in his tracks because he knows what a close-range blast can do.

Pointing guns at people that you can't legally shoot is a bluff. Even if the shotgun is 'scarier' than other weapons this is of limited utility. If you can't justify the shot it is still just a bluff.

The wound capacity of a load of double-aught buck shot (essentially eight .33-caliber rounds) is so devastating that 12-gauge shotguns are the tool of choice for professionals who must neutralize dangerous animals quickly without bothering to aim. When a commercial fishing boat hoists up a large and angry shark onto its deck, you can bet that the first mate will reach for his shotgun. When an animal handler at a zoo or circus sees that a big cat is about to attack, likewise he will reach for a shotgun.

(Emphasis mine)
This doesn't really prove anything. The professions noted aren't shooters, they are fisherman and zoo keepers. This is a bit like asking your golf caddy for medical advice. You do not have to aim any firearm if you are going to put the muzzle against the target. That is not particular to the shotgun.

And you know why? Shotguns don’t require precision and they are fearsome weapons at close range. I have examined wounds from pistols, and sometimes they resemble bee stings. Of course, the wound channel inside the body is bigger, but from the outside it’s sometimes hard to find the hole. In contrast, shotgun wounds are often horrific in their level of trauma. I’ve seen some that look like shark bites.

Contrasting the shotgun with a handgun is irrelevant. Nobody disputes that a shotgun is superior to a handgun. Comparing shotgun wounds to rifle wounds would be more appropriate. The M4 will produce relatively small entry wounds and 'shark bite' like exit wounds (if the round exits, otherwise all that 'shark bite' is on the inside.)

If you don’t believe that a shotgun is an excellent man stopper, consider that the eight pellets in your typical 12-gauge 00 buckshot shell tend to do some interesting things when launched in anger. For example, when fired at close range, they typically travel in pairs or in clumps into the body of the target. This effect rends organs and causes massive shock and blood loss.

The shotgun produces effects similar to multiple handgun wounds. Lots of small permanent cavities, while the rifle will produce one large permanent cavity.

Outside the typical range of close-quarter battle, shotguns can still be very effective. Spread patterns of shot fired from a typical 12-gauge pump make it more likely that you will score a hit on a moving target.

This statement means that you are only getting some of the pellets on target. The other pellets miss. So instead of eight .33 caliber handgun-equivalent hits, you are getting some number less that eight.

Of course, the effective range of a shotgun is much shorter than that of a rifle. That’s both good and bad. Shotguns are not a good long-range weapon. That’s absolutely true. But they also don’t create the overpenetration concerns that rifles do.

Overpenetration is when you hit something and the rounds exit. In the previous paragraph we learn that we are going to miss with some of the pellets. Those pellets don't overpenetrate, they just penetrate. Before you consider overpenetration as a concern you have to be able to keep all of the projectiles on target.

This does not mean that a shotgun doesn’t have to be aimed. Far from it; a shotgun must be carefully aimed. No police agency can accept careless, un-aimed fire. Police shotguns must be aimed and load centered for best results. And the hit potential of an aimed shotgun is considerably higher than that of a handgun or rifle.

Earlier the advantage was that shotguns didn't require aiming, but now they do - otherwise the spread will cause fewer projectiles to hit the target.

Under time limits, have officers of various skill levels fire at reaction targets or targets that involve some type of motion. You will find that your officers score more hits with the shotgun.

Reactive targets do not model actual fight stopping. Again if each pellet is a .33 caliber handgun round without good shot placement those are not going to be fight stopping hits. Also the above excerpt is comparing handguns to shotguns.

This article goes on to tout the shotguns ability to fire a wide range of special purpose munitions such as slug, breaching, and a number of different less-lethal rounds. All of which is true, but it is little more complicated than that.

Selecting the right round for the right situation is non-trivial. For most situations this is "select slug" for engaging targets at greater distances. Most law enforcement agencies flag specific shotguns for firing less lethal to avoid confusion (if an officer decided to fire less lethal out of his patrol shotgun other officers might think it is a deadly threat and start shooting.)