Vtyjkyuk

There is a list of at least 13 things that do not go into the compost pile. Most I know and understand. I just found a list that included potatoes.

Potatoes do what to a pile of compost? Feces, meats, dairy are obviously a no no but potatoes?

The only problem I can see is that a chunk of potato with an eye will grow. Is that the only reason?

I take it you're not Irish!

The only reason for not composting potato peelings is that they are a potential source of the fungus that causes potato blight. Blight spores can survive only on living plant material. Potato peelings can provide this when the buds in the eyes of potato skins grow into potato plants. To ensure that the peelings don't sprout, bury them well down in the compost and ensure that you turn the heap regularly. If you do this, it is fine to compost the peelings.

and ...

In most of the United States and Canada, Phytophthora infestans requires a living host to survive between seasons. Usually it lives in infected potato tubers, which can survive in storage or the soil (to become volunteers) after harvest or anywhere potatoes might be discarded. Tubers that have been discarded at any stage of crop production or handling (harvest, storage, shipping, spring cleanup, or planting) are known as "culls." Culls may survive if they are not destroyed (frozen, crushed, composted, or buried at least 2 feet beneath the soil surface). Infected tubers that are planted or cull tubers that survive the winter may be sources of the pathogen that initiate epidemics the following season.

https://www.gardenorganic.org.uk/faqs/potato-peelings
http://vegetablemdonline.ppath.cornell.edu/factsheets/Potato_LateBlt.htm

They can start growing again in the compost. That in itself isn't a big deal, since you an always pull up the plants, shred them, and recompost them.

The more serious issue is that you may be infecting the compost with assorted fungus and virus diseases, Potato blight is the most obvious risk but potatoes can also carry viruses that affect related species, e.g. tomatoes. Viruses will never be killed by composting - if you want to recycle the organic waste, burn it and use the ash. If you get potato blight fungus in your soil, it will take years to eradicate it.

Note, the diseases are carried in the leaves and stems, not just in the edible bits of the plant! Composting kitchen waste containing cooked potatoes is unlikely to be a problem.

I think it all depends on the temperature that the compost reaches. Cold will not kill a potato since they are exothermic; they store heat in their mass which helps them resist cold. Heat from a compost heap will dramatically weaken them - a good compost pile will reach 70 deg C pretty easily, weakening the tubers in the pile and making them vulnerable along with many fungi. And since at the time we are composting new potato haulms and recycling our old stored sprouty spuds there is plenty of fresh material going to the compost it's an ideal time to dispose of them. Right now my compost is running extremely hot with grass clippings, squash vines, spuds, ragweed, pigweed, ... A week ago it was six feet high, now down to three feet. A year from now when I use it there will be no sign of spuds at all.

From the point of view of an institution providing general advice, I guess they have to take into account all types of households: some will take composting seriously, keep a hot pile and will ignore the advice, others will end up with a slimy mess, a source of infection for other serious gardeners and the agriculture industry. It's probably best for general advice to err on the side of caution.