I am not sure if this is an Italian tradition or not? Maybe someone can enlighten me more on this subject; nevertheless, I will never forget the first time that I went over to my husbands house for dinner. His dad was such a great cook (like my husband lol). He prepared this spread of soup in a way that I had never seen before. He separated all the ingredients into different bowls and platters! One for the chicken, another for the broth, and then one for the little bitty noodles. It went on and on! There was a bowl of carrots, celery and tomatoes, too! Nowadays, when we prepare chicken soup, this is how we serve it for family and guests!
Very interesting, that almost sounds to me like some Asian soup preparations I've seen. One of them in particular called for thinly sliced raw beef and wulianned raw vegetables and fresh herbs, over which a piping hot broth was poured - everything "cooked" instantly in the bowl for a really fresh and fragrant taste. That's what the setup you described kind of reminded me of.
If I am making certain soups in advance, I will sometimes cook the pasta separately and add it shortly before serving the soup, so it doesn't become too swollen and mushy, and make the rest of the soup too starchy tasting.