So apparently -- not sure if this is a retroactive explanation or what -- we eat fish, soup, meat, and "compote," in that order, by all Shabbos and Yom Tov meals in order to symbolize the Four Worlds. (Source: I learned this today at my Chabad seminary. [I'm not sure if it's only Chasidim who think this way or what.])
Supposedly the compote (i.e., fruit-based dessert) symbolizes the highest world A't'z'ilus, which leads to the question:
How could we then, given this understanding, make a new bracha on dessert because "it is not part of the meal"?
It goes without saying that the Four Worlds are absolutely, inseparably connected.