The following are reasons to use a soup lid in Japanese cuisine.
1. It keeps the soup hot and keeps the dust away. Back in old days (i.e. three to four hundred years ago) in Japan, the kitchen was far away from the dining area, so they used a lid to keep the soup warm. A lid also kept the dust away while transporting the soup. At US restaurants, soup is served at the beginning of the meal, and it takes a few seconds to carry, there is no need to put the lid to keep it warm. In a modern kitchen, there is no reason to worry about getting some ashes from burning coal like the way our ancestors used to cook, thus no need for a lid either.
2. A soup bowl with a lid is for special occasions and special guests. Therefore, it's customary to use a soup bowl without a lid for regular meals at home and most restaurants in Japan. As such, if you were to go to a high-end restaurant like a Kaiseki restaurant, it's likely that you will be served the soup with a lid. Personally, I've never been to a restaurant in the US where they served the soup with a lid; I'm sure there are some who choose to use a cover for a more esthetic reason to treat every custom as a special guest.
3. Visually appealing and surprising. A soup bowl with a lid, generally speaking, is a clear dashi broth soup called Osui•Mono and not for miso soup. (Note: it's perfectly OK to serve miso soup with a lid and many will do so in Japan. It is not OK to serve Osui•Mono in miso soup bowl, though.) The reason is the element of surprise when a guest opens the lid to see the beautiful layout of the ingredients inside of the soup bowl. In Osui•Mono, you can see all the ingredients in broth, sitting at the bottom of the bowl, beautifully laid out, while Miso Soup, it's difficult to see the bottom of the bowl.
Again, unless the meal is for a special guest or a special occasion, there may be no need to use a bowl with a lid, especially lacquerware soup bowls with decorations that are relatively expensive. Also, just like a Japanese tea ceremony, I'd guess that many people in the US are unfamiliar with this practice. Therefore, many restaurants feel no need to spend extra dollars for the decorated soup bowls.
4. Aroma. What we think of as "flavor" is a combination of taste and aroma. While there are only five tastes, according to a recent study, a human can smell almost infinite combinations of aromas. While the exact number of how many combinations of aroma a human can detect is up for a discussion, the Japanese understood the importance of aroma in their cuisine. The lid on a soup bowl shields the aroma in a bowl and releases it when the user opens it. With miso soup, it's difficult to smell the subtle aroma of ingredients and dashi broth like in Osui•Mono, as the aroma of miso is dominant. Thus, many Japanese (chefs) may think it may be unnecessary to use a lid for miso soup.
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