I remember hearing about using potato peels to grow more plants. While I was preparing some potatoes to eat, I cut the skin along with some of the sprouts and some flesh attached. Leaving me 90% plus potato to eat. Getting both a harvest and a clone to plant.
That’s a old trick. It might have disadvantage that yield is smaller. Decent sized tuber can suport the plants better through variable weather. So you might need little more watering to get them established. Have no experience of this, but sometimes get volunteers from small tubers or pieces of tubers that don’t produce as much.
I have grown potatoes from just the sprouts, no potato attached. Yes, the potatoes are smaller. I see this more as a last-ditch effort to get some kind of yield if for some reason my seed potatoes are rotting or I have to eat them.
Lots of potatoes, but probably 1/4 the size.
I have planted potatoes the way you did and saw no discernible difference in harvest.