I think there are several issues.

The 12 ga gun was popular in England whereas the 16 ga was popular in German and elsewhere on the Continent. I think gun trends followed England and, after 2 world wars, German things were not very popular.

In the age of black powder, the 12 ga just out performed the 16 ga. I think that image has stuck in the minds of American hunters.

There is no 3-inch 16-gauge. Had that been developed, perhaps people wouldn't be swooning over the light weight 20 ga as an upland game gun.

Now on a personal level, I like a 16 ga and have hunted ducks and quail with one. However, if goose hunting with steel, I am using my 3 1/2" 12 ga.