Does your child's school use cloth napkins? Most Montessori schools do. How about at home? I know many families don't use napkins at all (cloth or paper) but I've found them really useful not only when the children first start with solids (weaning, baby led or Montessori style) but also for teaching grace and courtesy, just plain manners at the dinner table or when out at picnics or eating with friends and family (snack or morning tea).
We use our child-size cloth napkins every day. We are still using these which I made over five years ago. They have held up so well, and were absolutely worth the effort! I really love the variety we have. I've made them to approximately 8 x 8 inches. Although when Otis was weaning, the napkins I made for him then were much smaller (as pictured below). We also have a couple of these matching Montessori placemat and napkin sets from Michael Olaf. If you are looking to buy child-size napkins I love so many of the options on Etsy, I recommend searching for 'lunch box' or 'cocktail' napkins.
Children can be shown from a young age, once they start walking, to set their own table, especially if you are using a Montessori style weaning table. The child can wash, dry, iron and also learn to fold using the small easy to manage napkins! They like so many materials in the Montessori home, are child size, they belong to the child, they show the child they are special and loved! There is no need to stick to child-like prints, there are many adult prints and linens that children will enjoy too.