At talk with ship staff, someone suggested having washers and driers on board for guests, but thinking about it, I think it would be too hard to coordinate.
Many cruise ships on other cruise lines already have self-service laundromats onboard. Typically, they have washers, dryers, an ironing board and iron, and they sell powdered detergent packets.
Some cruise lines charge to use the machines, while some upscale cruise lines do not charge. These laundromats are not always located on every floor; some are on every other floor that has passenger cabins.
I never had a problem finding an empty washer or dryer, except for the last day onboard, when everyone seems to want to wash their clothes before returning home.
Royal Caribbean doesn't have these self-service machines.