It takes a large colony to use all 12 frames. It’s been a while since I read Brother Adams book, but I seem to recall his reasoning for going to 12 frames was to encourage larger colonies, larger foraging forces and hence larger honey yields. He also used deeper Dadant style brood frames. Brother Adam did a lot of experimenting and keep bees for about 80 years so I figured he
almost knew what he was doing.
However it’s a much different climate in the UK than it is here, so what worked great for him doesn’t necessarily mean it would work as well for all the different climates we have in the USA.
If you’re leaning toward an all medium setup which seems to be a modern trend, you would probably want to think twice, or more, about going to 12 frames wide because of the weight. Brother Adam used shallower supers to keep the weight somewhat reasonable. But if you mix mediums with shallows, then you’re back to the interchangeability problem the all medium folks seem to obsess about. I suppose a possible solution to that problem might be to use 12 wide mediums for the brood and reduce to 8 or 10 frames for the honey supers.
I run medium framed nucs, a few medium framed hives, and large brood frames for the rest. Medium supers for everything.
For the hobbyist the best design is probably the one that is easiest for the bee keeper to manipulate because the bees don’t care that much; they’ll make do.