IMO, after doing alot of research on the net I've concluded that the shotgun is a "niche" firearm, compared to a handgun and AR-type rifle. In the former, the shotgun best used to dominate the typical "pistol" arena in a short-range (0 to 30 yards), and the more CQB home defense environment with it's well-known fire power, albeit with some negatives.
Some thoughts gathered in my research.
1) Treating a shotgun like a big rifle with a limited range (100-yards +/- 15 yards) is a good way to use a shotgun loaded with slugs. But in order to be efective a user must have a sight tuned for slug use.
2) Treating a shotgun like a big pistol with a limited range (25-yards +/- 5-yards) is a good way to use a properly choked shotgun loaded with buckshot.
3) Treating a shotgun like a game getting weapon with a limited range (30-yards +/- 5 yards) is a good way to use a properly choked shotgun loaded with shot sized to your target.
4) Training people to safely use a shotgun to effectively kill game or dangerous threats (bears and/or people) takes less time than training people to use a handgun or a rifle which can take more time.
5) Shotguns are 50-state and virtually all jurisdiction legal for hunting, sport-shooting, and personal defense.
BUT there are noticable limitations of the shotgun:
1) Shotguns have limited capacity and therefore require more practice and more awareness for loading/reloading.
2) Shotguns have higher recoil than rifles and may make shooters with little experience less effective in shooting them.
3) Because of legal limitations, most shotguns are generally quite bulky, with some ezxceptions, and virtually impossible to conceal on one's person in an easy fashion, and are not legal to carry loaded in many places where a handgun might be.
4) Ammunition is bulky and reloading typically takes a longer time than an AR-type rifle and/or handgun. In this case, a user must have some back-up to provide cover in order to reload, or have sufficnet hard-cover in order to reload. Also, a shotgun user may have to disengage sooner when on-person ammo runs low.
Therefore, the shotgun can serve as an overmatch at pistol distances via improved hit potential and significantly greater terminal effects. The shotgun fills the same niche as a PCC, not the same niche as a rifle with greater range capability. With proper ammo it can be a superior to a handgun for shooting into vehicles at short range.
In comparing a rifle to a shotgun. If you aren't engaging a high number of threats, potentially wearing body armor, or in heavily fortified structures, a shotgun is probably the right choice (unless targets are at distances longer than 100 yards). That's a lot of qualifications for a police officer who may encounter that. By contrast for the average home owner sleeping in their bed at night? It's far fewer qualifications.
Shotguns are 50-state and virtually all jurisdiction legal for hunting, sport-shooting, and personal defense.
IMO, a proper self-defense shotgun is a tool to complement, and dominate the pistol distance envelope,but a user must understand it's limitations.
My .02