US Shotguns effectiveness is very overstated. Firstly they were issued with paper shells that in damp conditions like a french trench would turn to mush and jam the gun. Secondly combat testing occurred June 1918.

While in ideal circumstance it could be effective on the attack the inevitable counter attack would highlight the poor range compared to rifles and single shell loading over stripper clips meant they also had lower effective fire rates. They were very niche.

Actual usage rates are also much lower than you would imagine. Only 3500 Remington 1910A, 1500 winchester 97 "longbarrel" were sold to US army. The actual "trench gun", the modified Winchester 97, had 5000 units available in June 1918, 4000 going to prison guards, 1000 for combat testing in an army of 4 million men. By September it was 15,000 received out of an order 35,000.

The US army in 1914 was small, and american weapon manufacturers were busy making rifles for entente powers that when the US formally entered the war they had more recruits than rifles and needed weapons. While the 1903 Springfield was officially the standard issue weapon they used M1917 Lee Enfields, a british design was used more because they were available in the numbers needed. Buying shotguns to give to prison guards and rear echelon troops freed up more rifles for front line troops.

So why didn't Germany use them? Well because they sucked. Germany was suffering from material shortages including weapons so starting up production lines for new weapons, new ammunition types and new logistical lines would not be possible. It would mean diverting material away from proven effective weapons. The MP18 used existing pistol ammo and existing magazines.