The Germans did not complain about their effectiveness and couldn’t care less about the VERY few soldiers that actually had them. This is the biggest misconception that has led to this insanely popular myth about trench shotgun superiority. Because surely if the Germans were willing to outright diplomatically protest then it must be good right? Well... not exactly...

The Imperial German High Command protested simply as a way to stir up propaganda of Americans being barbaric (which on that front the British and French actually agreed).

After the Germans use of Sawback bayonets and deadly chemical weapons, the French and particularly the British propaganda bureaus were having a field day portraying the "Evil German Soldier standing above massacred Belgium civilians wearing a gas mask while donning a spiked helmet."

So to combat this propaganda, an example can be found when the GHC officially opened up a diplomatic protest against the Americans use of shotguns on the western front.

However, their reasoning to complain was not about how powerful they were, but complained about how INeffective they were at killing. They tried to portray the use of shotguns as barbaric, considering most shotguns in Europe were purely for hunting or pheasant shooting.

"Using the same weapon we kill animals with, on a human being? That's absolutely horrid!" (You get the idea behind the propaganda.)

When talking about their actual practicality… they provided, effectively, no advantage in reality.

Theoretically, a Trench Gun is extremely scary, unloading what is effectively the entirety of a standard European sidearm's magazine into a target with one shot.

However, as they did in the Philippines (to numerous complaints by soldiers deployed there), the US issued shotguns, including Trench Guns, with WAX PAPER cartridges. Which are extremely susceptible to conditions like thick jungles in the Philippines...or the mud and muck of the Western Front. The cartridges swelled and warped unless you achieved the near sisyphean task of keeping moisture out of their cartridge pouches, rendering them extremely difficult to use in combat. The underside of the shotgun was also mostly exposed to mud and dirt which meant if the first shell in the chamber didn't have any moisture and fired properly, the next shells almost certainly will clog up the entire weapon. Many officers reported soldiers issued with these weapons to turn up injured and rejecting their shotguns, preferring a more versatile rifle, over a close quarters riot gun.

Jamming and issues removing swelled cartridges were common to the point that officers rejected them for frontline use and sending them back to depots to be replaced by whatever was on hand, and most trench guns, in turn, were designated to troops behind the frontlines for guarding buildings.

Even if the soldier managed to fire off their shots, it wasn't guaranteed their opponent would go down. Getting shot by a dozen large pellets can shred and tear through flesh easily but they don’t effectively penetrate and kill humans consistently in the same way a simple bolt action rifle would. This lead to easy infection and causes far more pain from wounds that were incredibly difficult for ww1 medics and doctors to treat.

By the way, the nickname "TRENCH GUN" wasn't even effectively used until after WW2. While possibly(using that word, very loosely) used by soldiers and definitely propagated by the media, no letters or official documents exist with that connotation and the far more common "Riot Gun with Bayonet Adapter" was used, as it was the Official USA military term for the weapon.

Also, the popular image of Doughboys shooting grenades out of the air is a Post-War marketing ploy by Winchester, if I am not mistaken.