Well, you can buy a brand new 16 gauge Ithaca 37 if you want to.

FWIW, on the Ithaca website, they don't show or indicate a 16 gauge offering, however, if you download their Model 37 Specifications, those charts do indicate 16 gauge being offered.

Also, Winchester quit making the Model 12 "back when" because of the high cost to do so, and stsy competitive.
The majority of Americans want CHEAP, sportsmen are no exception. Maybe Browning/Miroku would offer some limited runs once in awhile (??).