Why using low temperature cooking for potatoes?
Cooking times are related to the type of tissue. A potato is a part of a plant, but an unusual one, an asexual bud.   

A potato is not a stem or leafy part of a plant, so it's not a vegetable. It contains no seeds, so it is not a fruit.  It lacks the protection of an external fruit sheath, and it isn't a fertilized ovum, so it isn't an underground seed like a peanut (legume) even though it can grow into a plant separated from it's parent.  It isn't a thickened root like a carrot. It's a thin-skinned tuber with a very high and available starch content and low cellulose content compared to vegetables, fruits, stems, root and seeds.   

The low cellulose content means that less heat is needed to break down the cell walls. The high starch content means that there is a short time between the cell walls breaking down, the starch quickly becoming available in large quantity and the starch binding with water to link into longer molecules, the reverse of what happens to meat protein that is gradually broken down during cooked. 

Lowering the cooking temperature increases the cooking time and the brief window of opportunity for removing the product from heat at the desired texture.