I personally think a shotgun is a VERY viable, versatile weapon. I also think it's one of the best survival tools and i'll never ever be without a shotgun. I may be slightly biased since I grew up in a state that only permitted deer/turkey hunting with shotguns but still, look at everything a shotgun can do! Its amazing the different ammo types and roles a shotgun plays!
in a fighting role, the shotgun is secondary to a carbine. shotguns have less rate of fire, capacity, heavier munitions, and less range. id much rather have a carbine in all environments, even indoors.
however, it feeds a great variety of ammo (can shoot slugs against larger game animals . . or motor vehicles), and is more practical in gathering some types of food.
I agree with you that a carbine is a very potent firearm. Lets compare these two in a given situation. 20 yards indoors or out, 30 carbine m1 115 grain grain fmj vs 12 ga pump #1 buck. Both projectiles are app. 7.62 diameter, one pull of the trigger delivers 1 carbine round at a higher velocity and the shotgun delivers up to 30 at a lower velocity. M1 carries 15 round mag and shotgun carries 6+1. Bottom line IHMO is that if you have the carbine, dont let the bad guys get close and if you do, have a shotgun.
In normal home defense situations, nothing beats a 12ga loaded with 00 buckshot. Shotguns are simple to use and easy to learn, plus the proven track record of 12ga buckshot speaks for itself.
Sure, the carbine can have its place, but they are usually more complicated, intimidating to the casual shooter, and require extra training to be used effectively. I believe the carbine is best used by those with more exposure to it, such as LEOs or the dedicated shooter.
At least with shotguns, the type of action can be tailored to the shooter's level, with a broader range of choices: single barrel, double barrel, pump action and auto loader.
With carbines, it has already been shown that shot placement becomes more critical due to the lack of general "stopping power". Shot placement is key no matter the situation, but what would normally drop an attacker faster with a single shot; a 12ga or a 5.56mm? With 00 buckshot, a standard 18.5" barrel with a cylinder bore will put all nine pellets in a circle the size of a fist at standard "in-house" distances. That is the equivalent of being hit with nine .38 special bullets at the same time.
In the end, due to what I said above, I have always had a 12ga. It is my first line of home defense (when I need a long gun) and I don't have any reservations about that decision.