Many municipalities disallow laundry chutes in new home constructions. They can create a chimney effect allowing a fire to travel faster between floors. Also kids like to play with them and not all kids are smart enough not to try and slide down it.
BTW, build it with the assumption that it will get soaked in disgusting things. Drywall isn't strong and isn't really washable. Non-stick coatings are best; metal is OK.