The potato plants in my garden have taken the unusual step of fruiting. Most gardening books say you should just discard the fruit because any potatoes grown from them would be completely unpredictable mostly primitive throwbacks (although I presume edible). Each pod is supposed to host 240 seeds, each with it's own genes.
Would it be more paleo/healthier to grow and eat the primitive although I'm guessing less tasty potatoes next year rather than more of the cloned Yukon Golds that have the fruit set on them? Should biodiversity for biodiversity's sake trump convenience and tastiness when thinking about the future of our food supply?
Personally, I love the volunteers that sprout up in my garden. It's a thrilling guessing game how they might turn out. Sometimes they are disappointing, other times rewarding. I tend to favor these plants with a little extra love because they add an element of chaos that is always welcome in my life and my garden. If you have limited space, you might want to make room for something else that you can better predict the outcome of, especially if you tend to grow hybrid potatoes. Otherwise, add a little randomness and let those babies fruit! The most oft stated reason for pulling volunteer potato plants (if they are heirloom potatoes that are the same from one generation to the next) is that blight is spread generation to generation and can destroy your whole crop if the plants are infected from the previous year.
I can't speak for the nutritional value, but for me the element of surprise makes it worthwhile. This year I have several mystery plants that I'm tending; A tomato, some possible squash or pumpkins, and volunteer potatoes that sprouted up in my potato baskets that I must have missed from last year's harvest.
I have never heard the part about the descendants being inferior throw-backs. This year, I am growing and saving my potato seeds on purpose, with the hope that I will get some interesting varieties that may also be better adapted to my particular climate and soil conditions.