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.