It's mostly the latter, it also helps a lot that potatoes are pretty micronutrient-replete and low calorie density compared to other bland, starchy staples. I would expect a diet of nothing but rice, steamed chicken breast, and steamed broccoli to have similar effects. This is of course close to how physique enthusiasts have learned to eat to lose fat.
Here is Stephan Guyenet writing about the diet 10 years ago: http://wholehealthsource.blogspot.com/2012/12/the-potato-diet.html
The potato diet works for well-understood reasons that are entirely accounted for by mainstream obesity science. The brain's appetite regulation circuits are highly responsive to calorie density, macronutrient variety, salt, food variety in general, and other things which are all minimized by eating only potatoes. The putative connection to lithium is grasping
The reasons are well-understood. It hasn't taken off because eating nothing but potatoes seems extreme and weird to most people, and even less appealing than other diets