I tend to read accounts of people trying a "potato hack" where they adhere to the diet for only a few days, or a week, then go back to regular food. They often lose a small amount of weight but don't move the needle much.
Then I read accounts of people who do it for months, very strictly, and they usually lose dozens (sometimes upwards of a hundred) pounds, and keep the weight off with little effort.
If the potato diet actually needs to be accompanied by a significant amount of exercise, it's probably mostly just another fad diet that is tricking people into losing weight themselves. But, Penn Jillette famously ate only potatoes for 4 months, never exercising at all, and lost over a hundred pounds. Those are the specific kind of claims that need to be verified (or falsified) here, if a large-scale study is ever done on this.