I don't think I've seen a single washer and dryer in all of 3 and New Vegas. My experience with the first and second games are very limited, so I can't say for sure there. No laundry rooms, either, or laundromats. Tenpenny Tower didn't even have a laundromat. None of the new settlements have clothes lines or wash buckets/boards lying around. Do they have fabric that never soils?
Thread for oddities, inconsistencies, and oversights in the world and lore.