the mind idle as it is during potato peeling, I wondered how to improve on the potato peeler. The first draft is a machine in this crude diagram.

In my first draft, the idea is inspired by an electric beard razor. Unlike the razor which moves whilst the face is kept still this device moves the potato with the devices held firmly in one hand.
There are three parts to this idea. The cylindrical tube like frame allowing the potato to be pushed against by hand. A set of several spring mounted cylindrical blades pushed against the potato to perform the peeling function. The third part are the spring mounted sprocket like wheels that roll the potato in the hand.
The user would hold the potato lightly in the cusp pushed against the tube end. The spring mounted sprocket will push the potato along and the spring mounted blade cylinders perform the cutting of the skin. With a bit of practice I believe on can move the potato so that it gets shaven evenly all around.
Unfortunately, just like the manual peeler small folds and small concave dents will not be processed very cleanly either. But I can imaging that given the right speed and traction of the sprocket the peeling can be done quite fast.