I have one without removeable plates and use it often. When I take the meat off the grill and turn it off, I leave the lid open so the bits left of the grill won't continue to cook and burn.
When I start cleaning up after eating, I wet two or three paper towels, place them on the bottom plate, close the lid and turn it on for about a minute then turn it off. After I finish the rest of the dishes, I open it up and just wipe the plates. The water and heat sort of steams it clean.
It's kind of like putting a cup of water in the microwave and letting it boil for 5 minutes. Leave the door closed for another 5 minutes, then open and wipe it clean. Easy as pie!