There "Have Been" 3" 16 gauge guns. In fact I have one, a 16 gauge H grade Lefever with 3" chambers. If memory serves me correctly it was in the late 1970's I was at my favorite gun shop of the time & a gentleman brought in a fired 3" 16 ga Remington Express SP hull he had found while deer hunting. He was in the mountains in one of the few areas in TN that holds a few grouse, so was possibly used for one of them. It was marked as 3 de-1˝ oz #7˝ shot as I recall. Wondered at the time just why anyone would want, or need, an ounce & a half of #7˝'s. Generally speaking by the time the pattern is getting too thin with an ounce of 7˝'s you need to be going to a larger shot size.
Anyway I would love to see the 16 make a grand comeback, but seriously hope an extra length "Magnum" version never catches on.