The shotgun in WWI is more myth than reality, its legendary status the product of two competing propaganda machines as apposed to it's actual effectiveness in combat. I won't be going into the protest by the German government, that's been covered elsewhere, but suffice to say the protest had more to do with portraying the Americans as savages to the German public more than actually stopping the Americans from using the shotgun. On the American side, popular media portrayed the shotgun as a wonder weapon, despite many of these stories coming out before American soldiers saw combat in the conflict, and those that were based on true events we often massively exaggerated. So why did the Americans use shotguns in WWI while no-one else did?

The story really starts in 1886 with the French adoption of the Lebel rifle. Prior to this, the militaries of the world we're using large bore black powder cartridge rifles, either single shot or early repeating actions. The French, with the adoption of the Lebel, basically rendered all rifles then in use obsolete. Poudre B was the first smokeless powder to be used in a military rifle, and pairing this new powder with a sleek 8mm bullet meant the new French rifle could shoot farther, more accurately, and hit with more energy than anything that came before it, all the while eliminating the "fog of war" generated by black powder. European powers scrambled not to fall behind the curve, quickly rearming in the 1890s and early 1900s with new rifles using the new smokeless powder and sleek small bore bullets.

This massive rearmament meant that there were millions of these older rifles and tens of millions of cartridges left in service. Prior to WWI these rifles were generally left in storage, used for training purposes, or issued to loyal indigenous forces in the various colonies around Africa & Asia. However, once the war broke out basically all the major combatants in Europe had shortages of arms from the massive losses sustained in the early part of the conflict. These older rifles were brought back into service, largely issued to rear echelon troops like guards, artillery crews, messengers, veterinarians, etc, basically anyone who wasn't expected to be in combat but needed a weapon for self defense should there be a break in the line and their position was overrun. By giving the rear echelon troops these older rifles, it freed up standard service rifles to be pushed up to the front to be given to the soldiers that really could use them.

Just like every other country, when the US entered the war they had their own shortages of small arms. Unlike the powers of Europe constantly squabbling amongst themselves in late 1800s, the US really didn't have a major military since it demobilized after the Civil War. Therefore the US didn't have vast quantities of rifles it could draw on to sure up it's supplies, other than a handful of rifles left over from the Spanish American war.

What the US did have was the shotgun. The Winchester 1897 and Remington Model 10 were already popular & well proven guns by sportsmen in the duck marshes of North America, and there were thousands that could be bought immediately by the American government on the commercial market. On top of that, Winchester and Remington already had the industrial works set up to produce these guns, so other than a few tweaks desired by the military (like a heat shield and bayonet lug), these companies could immediately start producing new guns without having to spend time building new factories & tooling. Finally, shotguns use smooth bore barrels and shoot very low pressure cartridges, so shotguns are also significantly cheaper to produce than a standard rifle.

While there are definitely more than a few cases of Americans with shotguns winning the day, by & large the shotgun was generally not well liked by soldiers who were issued them in front line field trials. The shotgun ammunition issued in WWI was loaded in paper cases, and in the extremely wet conditions of the trenches the cases would swell & cause the gun to malfunction. On top of that, the buckshot loadings dispersed quickly and lost energy rapidly, so while devistating at close range, if the fighting extended beyond 50 yards the shotgun was quickly outclassed by the service rifle. Final, the loose ammunition was much slower to reload & harder to carry as compared to the box magazine of a handgun or stripper clips of the service rifle.

These issues meant the shotgun was largely relegated to second line roles, being issued to prison guards, soldiers on night patrol, and other auxiliary troops, just as the US military intended it to be. The other powers of Europe didn't consider the shotgun because they already had rifles to fill the same role, and didn't need to spend the funds on shotguns when that money & production capacity could easily be spent on other wartime essentials.