I'm guessing you're not European from this comment. This is not meant as an attack; it just seems like your comment lacks the perspective of actually living in the EU.

EU law makes news. It doesn't make many obvious appearances in day to day life when you're living there, however.

From my perspective, EU law does not play the most dominant role in everyday life. Apart from the big (or super silly) changes, it’s often more of a news maker. Take that plus big cultural differences (most notably: not being able to understand each other’s language), and you get a feeling of own nationalities.

There are still so many cultural and legislative differences between countries that people don't feel Europeans, they identify with the individual country.

The UK was definitely the country which stood out the most in EU, so after Brexit, the EU lost one furthest away country in its block, in terms of diversity.

EU law cover stuff you hardly run into. Sure, you have euros everywhere but they don't regulate how much taxes you pay or how your national health care is managed.

All is fine until they start regulating on things that matter. Immigration is definitely one of the first sector where people started noticing they're in the EU, because they're unhappy with the results.