Hi Brian...
Ok, I'll be glad to go there. But my disclaimer is that this is opinion (based on observation or digestion of what the old time gun scribes talked about).
The 16ga was pretty much the perfect shotgun for many, many shooters circa pre-WWII. A few significant and widespread things happened postWWII that hastened the 16's downward slide but - to answer your question first -
Ithaca was the last of the major manufacturers to drop the 16 from their primary gun (the 37). In fact, they produced goodly numbers of them into the 70s whereas the other big makers had drastically reduced their 16 production by about 64 and had pretty much dropped the 16 from their primary models by the late 60s. That's why you can still see so many of the venerable Ithaca 37 in 16 ga today.
Pivotal events that made the 16 "odd man out" include the ammo makers wanting to eliminate that inventory unit because its' sales was not supported by any of the clay target games - meaning way low volume compared to the other gauges. Another factor - prior to WWII the American homeboy who hunted with a scattergun was usually after grouse, quail, rabbits and squirrel on the home place and the 16 was/is THE gauge for that stuff. But when GI Joe got home with his rifle and money flowed like spilled shot, he got in the family sedan and headed for the deer woods or the pheasant fields. In the case of the latter, the ammo makers quickly announced you needed a 12 ga (Remember, Marketing Depts are not required to speak, or even know, the Truth).
On in the 60s the concept of the Magnums and Baby Magnums and that whole schmaltz erupted from the Marketing Dept - in both shotguns and rifles and pistols. "Magnum" meant sales and magnum song was a din so loud you couldn't hear yourself think. The real hoot in all of that was the makers trying to convince the Public of the wonders of a 20ga Magnum which tried (but didn't succeed) to be a 16ga.
But - that's how things work sometimes. We discard something good, replace it with something not as good, and call it Progress.
I have a great 16, one of the very first Bill Hanus Birdguns (made by Ugartecha and bought about 1988 aprox.) . For anyone who wants some authoritative discussion of the 16, here is Bill's website:
http://www.billhanusbirdguns.com/archive.html
Enjoy !