Chain moves side to side with gear changes, and adding extra chain tension with an extra drive sprocket could make the deraileur angry. Also, chain-tube geometry varies a lot. Not impossible, just more complicated than it might seem.
I ride an all-original 1970s steel-frame road bike, which seems like a prime candidate for this sort of product. I'm certain no sprocket-based design would fit it. I'd buy one of these if there was any way to lock it up.
Yes, but a tiny minority of bikes use those, and the product is meant to go on existing bikes. Also, even on hub-geared bikes (or single-speeds) you’d still need to switch to a longer chain or significantly move the rear wheel to be able to mount the powered sprocket in the right place, so that it wouldn’t skip.
I ride an all-original 1970s steel-frame road bike, which seems like a prime candidate for this sort of product. I'm certain no sprocket-based design would fit it. I'd buy one of these if there was any way to lock it up.