It's an interesting idea, but the end result would probably be less options for people with allergies (unless they risk foods that appear to be safe, but lack the label.)

We already have this type of labelling for gluten free foods, and one common complaint in the celiac community is that gluten should also be a major allergen. This would help greatly in deciding if a product is safe for people with celiac, since many products are but manufacturers don't bother putting GF labels on them.