It depends...
You can make a 12ga perform balistically like a 20ga with 7/8 oz loads / and you can even make it balistically like a 28ga with 3/4oz loads ( especially if you reload ). So in that sense, a 12ga - means you don't need a 20 or 28ga ....especially since these days, with screw in chokes - with a 12ga you can go from a Full to a Skeet choke, and everything in between and pretty well do anything you want to do with a 12ga.
20ga guns can be loaded up to a 1 oz load / lots of loads around - and although I doubt you can get 1 1/8 oz of shot into a 20ga shell - being able to go to 1oz makes a 20ga pretty versatile too - and you can load it down to 3/4oz or even 1/2oz ( like a .410 ).
12ga guns used to be heavy and bulky / 20ga guns used to be a little lighter and swing a little faster - but all that is gone today too. There are some 8 1/2 lb guns made in 20 ga (just like a 12ga ) - 30" barrels are common on 20ga's , etc and with screw in chokes you can go from Full to Skeet and everything in between with a 20ga as well.
in the 50's and 60's - before screw in chokes - we all had a "waterfowl gun", we had a "pheasant" gun, a "grouse" gun ...etc . We bought guns with fixed chokes / different barrel lengths that suited the intended game we were shooting or hunting. So some of the nostalgia for 16ga, 20ga, 28ga etc is from those days. In the 50's and 60's there was not a large variety of shells - so we really couldn't get lighter ( 7/8 oz loads for a 12ga ) especially if we lived in rural areas.
Today that has changed - but personally, I'll never get rid of my 20ga, 28ga or .410 guns. I like shooting them all - and I like having them ... and there is something really specail about going out Quail hunting with a nice 28ga Over Under that just brings a smile to my face. Some guys feel the same about S X S's ...
I don't think the 20ga is going anywhere - and it will remain a very popular gun. It has nothing to do with cost / most Over Unders in 12 and 20ga are about the same price. I don't watch prices on Mossberg pumps, 870 pumps too much - so there may be a disparity in their prices on 12 vs 20ga guns / but the Browning BPS is the same price for a 12 and 20ga version - at about $550 list / and they charge about $40 more for a 16ga, 28ga or .410 version.