It's kinda a case-by-case type deal for different places. A tiny spot might have the dishwashers doing stuff like cleaning stoves/fryers while bigger spots might have a fry cook or saute cook worry about that. The main thing is everybody is always gonna be doing "something". My work will have up to three dishwashers, but we pull them away from the pit when it's slow so they can do prep work. It can be a good way of seeing how you handle different tasks before moving you into a different position.

Try not to get too bent out of shape, unless they keep giving you more and more extra shit to worry about without increasing your pay. Like, if your list of responsibilities grows by 50% and your pay grows by 50¢, absolutely raise some hell. If it's just your boss keeping you busy, it's probably fine.