For most in house uses I see, the shot column would only open up to about 7 inches in a cylinder
bored gun. I "think" that would be dead adversary if you are
using a 12 ga.
If I'm in error, please educate me.
OK, let's try...
A shot pattern of about 7" is a little generous for most shotguns. Not unrealistic if you include absolutely every pellet. At least you're thinking reasonably. But this is for a 10 yard shot, most will be a lot closer.
The gauge of the shotgun is irrelevant. 1oz of shot from a 20 gauge is the same as 1oz of shot from a 12 gauge. The difference the gauge makes is in how much shot you can cram into one shell. The short version is you can get more in a 12ga. People think a 20ga kicks less than a 12ga because the standard 20ga load is only 7/8oz where a normal 12ga load is 1 1/8oz. It should be obvious that more mass equals more kick. There's a lot more to it than that, but that's it in a nutshell.
Why does 1 1/8oz of #7.5 not do as much damage as 1oz of 00 Buck?
The answer lies in the individual pellets. Looking at the chart above, we see that a #7.5 is only .095" in diameter while a 00Buck pellet is .33" in diameter. Basically a .1Cal vs a .33Cal projectile. Bigger equals more impact and better energy transfer.
Once the shot leaves the barrel of the shotgun, it starts to spread. Not just sideways, but lengthwise as well. So when it hits the target, each pellet has to be counted as an individual. You don't get better penetration just because there are more of them. The further away, the greater the affect of the spread. The more time between impacts, the greater the chance the target has to recover. At very close range, a yard or less, the 400 pellets from a 1 1/8oz load of #7.5 will do some serious damage. No one doubts that. But a load of 00Buck will do more damage because each individual pellet carries so much more mass.
At 10 yards, it's unlikely that a load of #7.5 shot will kill someone. If shot in the face, it would probably stop them, but if you miss...
At 10 yards, it's very likely that 9 pellets of 00 Buck will hit a vital organ and stop someone.
If you're pointing a shotgun at a bad guy it's because they're threatening your life. If you're life is on the line, do you want a tool that will probably slow the bad guy down? For me, I want the one that will guarantee a stop if I do my job and put a round on target.