I don't think I've ever had them mold/rot on me (unless they were in plastic packaging). They usually start growing before that, and I'll sometimes plant them lol.
I’d get them in plastic, and try to cut the top side of the bag all open within a few days, and often I get through them all without problems but sometimes not.
I do now have a plastic container I could dump them in that could be an improvement. I’ve thought of cardboard boxes but I imagine spores getting into the cardboard for the next potatoes and maybe moisture from the potatoes being a problem.
My mother kept potatoes in a plastic container in a cabinet, but I don’t know how well they kept or how quickly we used them up.
We grew all kinds of vegetables growing up, and potatoes were one of them. We kept them in a big wooden bin in the cellar and they very rarely, if ever, rotted between seasons. Would use what was left over in the spring for planting (a lot of them were already growing by that point lol).
Moisture is an issue. Dogs knocked their water dish over, and some of it went under the door into the pantry where a bag of potatoes was sitting. I didn't notice it for several days, and those did rot. Rotting releases more moisture which spoils any adjacent, and so forth.
So I guess as long as they stay cool and dry, they're golden. Though once they start sprouting they're less ideal to use for cooking (and difficult to peel, too).
I have no idea, TBH. I've always bought them in bags where they could "breathe", and those all eventually start growing (rather than rotting/going bad) if I forget about them in the pantry for too long. The only ones I've ever bought that were plastic-wrapped were big, baking potatoes. Maybe it keeps them from sprouting for a bit longer?
Eh maybe it's a moisture thing, where locking in the moisture saturates them in their own funk? Cause yeah I'm with ya, I usually buy the mesh bags and they'll keep until they start gaining sentience.
Some may have some spots that look like rot but they're very localized. Never had mold I don't think. Some cut ones had some white on them but that didn't seem to become fuzzy.
I don't think I've ever seen potatoes sold in plastic though - unless you mean plastic nets, but I assume you mean like actual plastic bags or something. I empty mine on like a double layered cover of an old fan, so it sits in a big pan of grating basically. No active ventilation though.