I can see why that never caught on. Interesting concept though. Very similar to the heated pots used on self service counters in buffets to hold soups, stews, oatmeal on breakfast bars etc etc etc
1. Solution in search of a problem. I’m mean what real advantage did it give over a normal burner?
2. Extremely difficult to clean if that deep well got the contents of a boiled over pot or a spill under the element.
3. Mechanically complex. You don’t want to have moving high temp elements if you don’t need them.
4. Obviously required specific pots.
I remember those open ring stoves here. They were never much of a thing in continental Europe, but in Ireland and Britain, before ceramic tops were popular those open rings were the norm, as they heat and cool a lot faster than solid rings.
I just seem to remember them being a cleaning problem. Our Creda stove lifted up, much like a car hood, and there were some kind of removable trays or maybe it was one big tray (I can’t remember the exact details) however it was always a mess if something boiled over or fell through the ring.