A fair question, and finding a substantiated answer seems rather difficult, I don’t even have anything covering the unit basis of issue of shotguns in WW1.

However, what I can find indicates two different reasons covering the coming and going of shotguns: Obsolesence and ammunition.

The advantages of the trench gun in close quarters combat is obvious: Precise aiming is not necessary for a hit, and in an environment when an opponent could appear at very close range, snap shooting is highly important. No other weapon in use could perform that role. A noted problem, though, came from the fact that modern plastic shotgun shells did not exist, they used paper casing. The paper did not react well to the damp conditions which could be found in the trenches, so the military started producing brass cased shells. They made so many of them that they supplied military shotgun needs through the banana wars into WW2.

The weapon which could perform the CQB role was developed at the very end of WW1; the sub machine gun. This compact weapon had a larger effective range than a shotgun, could perform an excellent suppressive fire function, and was well suited to operation in the close quarters battle. Perhaps not as outstanding as the shotgun, but good enough, with other advantages to make up for it. By the time WW2 came around, the M1928 series Thompson machinegun (think Chicago gangster, but with box magazines) was on common issue in the US military. This was later replaced by the M3 “grease gun”, a cheaper, smaller weapon, plenty deadly in close quarters. Thus, there was no need in Europe, absent trenches, to use shotguns. FISH and CHIPS (Fighting In Somebody’s House and Causing Havoc In Peoples’ Streets, what the US calls MOUT) could be well serviced by the SMG and hand grenades. In addition, the same SMG could meet other roles, such as weapons for AFV crews, resulting in efficiency.

The notable exception was the jungle. Shotguns do indeed still seem to have been popular there, but after a while, there was a problem. That stock of brass shotgun shells the military had ran out, and the replacement ammunition which could be procured was, again, paper, and if they had problems in Europe with damp conditions, you can imagine the fun folks had in jungles. This likely soured a lot of folks off shotguns in favor of something else, like sub machine guns. Eventually the military started production of M19 brass cases shells, but I would wager a lot of damage was done. This stock seems to have lasted until the 1960s, and I ran across a website indicating that, yet again, the moisture problem with paper shells returned at the beginning of Vietnam.

These days, of course, we now have assault rifles and carbines which do a reasonable CQB job whilst simplifying issue. Shotguns have, however, made a return, but due to the range of ammunition they can fire (We even had one given to us as a tank crew in Iraq). Today military shotguns are likely to be used for firing door breaching rounds and less-Lethal rounds as much as for lethal purposes.