"I suppose the main attraction was that they looked easier to keep clean. Whether they actually were is another matter.
You may still find them on new hotplates."
Yeah, there are a few brands of hotplates with them, I've seen them at Sears and Walmart. I have a Walmart "Farberware" one with two burners (formerly under the "GE" Walmart brand.)
Plus the majority of commercial electric ranges use them. In that environment the retained heat probably helps, since they're left on for long periods of time.
The main issues I see with maintaining them is if they're not kept completely dry, the cast iron tends to rust. They used to sell some kind of product you would put on them and then turn on the burners to burn it in. I think a light coating of vegetable oil should keep them looking black and prevent rust as well.
I think the long preheat and cool down times are the main issues they weren't as good as traditional coil or even smooth top ranges, and hence went out of favor here. It seemed they were usually only seen on the "posher" brands such as Jenn-Aire, KitchenAid, and otherwise TOL models when the "Euro" look was big.
Guessing they are still popular for hotplates because of the easier cleaning, and smooth top radiant hot plates were never really offered until recent years here, and even at that don't seem nearly as popular as induction.