That is the idea. The point is to discourage those who have the greatest risk. If you can stop people with allergies from eating your products in the first place any cross contamination will never be relevant.

>I don't remember seeing "may contain" in the EU, i remember seeing "may contain traces of" which is information rich, it lets you know that there was that allergen in the factory for some other product so if you have that allergy don't eat it

Those are essentially the same statements. Just very slight variations of syntax.

The important thing though is that these statements do not mean the producer doesn't have to control for allergens. In both the US and the EU they do. It's a hedge to reduce risk.