According to epicurious.com: "It is important to have a clean stock before you add the other ingredients, because the foam is impure and should not be cooked into the stock; if the stock is not clean before you add the herbs and spices, you will wind up skimming them off, altering the flavor of the recipe."

Also, if you don't skim off the broth, it can become mixed throughout the stock as it simmers, making the stock cloudy and unattractive.