I agree it looks silly, especially on something we are as comfortable with as eggs.
I'm just not sure it's ludicrous application, rather a failsafe labelling mechanism. If the product contains egg it gets the appropriate allergen label, no need for any assessment or decision making, therefore no possibility of missing anything.
You can either call it fear of litigation or fear of harming customers, but if it works for them!
The name egg isn't reserved for just for actual eggs.
Personally, I'd rather companies apply labelling 'just in case' rather than second guess where that information is of value. Besides, it's probably just how 'their' labelling process works, insert product name here, weight, ingredients, contains allergens etc., there is probably very little link to 'what' the actual product is.
There may not be any H+S legislation that demands labels of that type, however EU REGULATION No 1169/2011 states that labels must declare 'any ingredient or processing aid ....causing allergies or intolerances used in the manufacture or preparation of a food and still present in the finished product....'.
Whilst this seems obvious for an egg, there are thousands of foods which would not immediately be expected to contain a particular allergen. If you have a serious allergy, with a risk of anaphylactic shock, this information could well be life saving.
The legislation prevents anyone from needing to decide when the situation is so 'obvious' that a label need not be applied.