One of the problems with Law of Land Warfare is that you don't want to inflict unnecessary suffering on your enemy.

It's kind of a, do unto others thing - to put it shortly.

One of the things the U.S. Military has moved to is rapid attack (blitzkrieg, if you will) across a battlefield with a quick transition to stability operations.

Unnecessary killing doesn't exactly support this, because the goal is to eventually give the country back to the people (politics aside, it's a whole different practice in real world scenarios)

Anyway - tying this back to shotguns in trenches - a shotgun is a cluster of small rounds that causes a very large entrance wound that is difficult to heal. Its spread patten makes exit wounds unpredictable and it causes a lot of internal trauma. It doesn't kill quickly, and it takes a lot of medical attention to stabilize a patient that has been shot with one of these weapons.

In modern high intensity conflict, you want to defeat an enemy. This means he either physically cannot attack you because you outnumber him, he is cut off from supply lines (think chessboard style) or he is psychologically unwilling to fight you.

When someone is shot on the battlefield, you lose 3 people. Battlefield math is kind of a term tossed around when it comes to analyzing tactical and strategic level combat - you want that superior 3:1 ratio on an enemy to ensure that even if he gets a 1:1 ratio of kills to losses on your forces, that your force is still ready.

A 5.56 mm round is not designed to kill quickly. It is designed to accurately enter a target, predictably spread (mushroom) and then exit. This forces you to focus on a treatable casualty in combat (1 person treating, 1 person securing, 1 person being treated) and then prep for movement to your ambulances that will require you to lose firepower at the tactical level (a fire team is now out of the fight by losing 1 team mate) that compounds upward when you have casualties. They pay off exponentially because people don't want to die. As forces treat themselves to save lives, firepower superiority on the attacker side increases.

Shotguns go against these fundamentals and are thus "unfair" (yes I realize there are worse weapons than shotguns, but this is the fundamental argument for not using them as a standard issue weapon in combat, they are still issued - I had one in Afghanistan - but this is the ideology behind why an enemy commander would view it as unfair instrument of war.)

Tl;dr - dog semen smoothies can't melt steel beams