The 16 faded because the 12 and 20 overlapped it's performance, and unless a gun is made proportionally for the gauge there is no advantage in any direction. The manufacturers were more than happy to stop making a different receiver/frame size as well. Very few new shooters out there looking for a 16. Everyone who loves or wants one usually already has one or more.
A lot of people love 16s, but I never got it, and I have shot a lot of proportioned 16s in different action types. For those who tout the performance with a weight advantage over the 12, I find a 20 will match the performance with even less weight, and for those who tout the recoil advantage I find lite loads in a 12 will do even more recoil abatement.
The fact that is isn't one of the four gauges recognized for registered skeet no doubt didn't help it either.
The truth is they just like 16s, and nothing at all wrong with that. I'm the same way about the .44 Special, and I have the same problem. Not enough market to make new guns widely available.