The Irish had milk also with all the potatoes. It made it a diet that could keep you alive and even thrive.

>Potatoes and milk, particularly buttermilk, were a nutritionally complete diet for many Irish peasants before the famine, allowing them to be healthier than some European counterparts who ate a bread-based diet.

Potatoes contain all proteins, if i'm not mistaken, only less than protein rich plant sources. Wheat and rice need to be combined with other sources to get all proteins.