I +repped your post, because you honestly make very solid arguments. However, you are mistaken regarding shotgun patterns. At ten feet, 00 buck is pushing 3 inches in diameter, 3" magnum closer to 4" pattern. This, opposed to an impact area the size of the tip of your pinky finger, is an advantage of epic proportions in a gun fight.
You are correct the shotgun is optimal within 50 yards, but that is well over the average of gun fight distances. And yes, many people have incorrect at how the shotgun does not require aiming. However, a single focal plane system (a bead on the end of the barrel) reduces aim times significantly, and the larger pattern allows for pulling or jerking while firing. In other words, fully agree in no way is it a be all end all firearm. But I would respectfully suggest you step back and consider that even small advantages are game changers in that kind of situation.