Shotguns are no more "point and shoot" thank ANY other weapon. Inside an out 5 yards, the shot will most likely be in a 2-3 inch circle. Shotguns don't spread like the movies, and there is no reason to advocate firing them differently than a carbine.
Loading the firearm with multiple types of ammunition is also dangerous. By doing that, you are trying to script your gunfight. If it isn't "time to get serious" when you pull the trigger the first time, you have no business shooting someone. #6 shot won't even penetrate my shooting glasses, let alone bone and large blood/air filled organs. The goal is rapid incapacitation. That is done by adequate penetration and proper placement. BIRDSHOT just doesn't reliably penetrate to an adequate depth.
A carbine does not have a 2-3" circle of potential impact. at best, a carbine shooting a 45 caliber projectile has a .452 inch circle of impact that must contact the assailant. that's less than half an inch, but lets round. Lets say that round magically expands to .5 inches. That give you roughly a 16% chance of the hitting the assailant vs. shotgun at 15 meters (which is actually 5" diameter, not 2-3"). a 223 round has a circle of impact of .224, or about half that of a 45. now you're down to roughly 8%
at 15 meters 00 buckshot typically has a shot pattern of roughly 5X5 with a cylinder choke. That circle expands with bird shot at the same range. but I used your 2"-3" circle for comparison.
So why advocate shooting a shotgun different than a carbine? because you DO shot a shotgun differently that a carbine ( or other rifle for that matter). you AIM a carbine/rifle/bb gun/pistol, you POINT a shotgun. It's probably why a shotgun has different sighting systems that a rifle. . . strange how that works. And yes, I know there are rifled shotguns/projectiles - we're not talking about those, we're talking about SHOT
So do you want to try to hit that guy coming in the window with a projectile roughly as wide as a pencil, or a projectile CLOUD roughly the size of a book. . . you can keep your carbine.