That argument goes both ways: each country in Europe might be smaller individually, but at the same time I can pay with my debit/credit card all across Europe,

That argument goes both ways: each country in Europe might be smaller individually, but at the same time I can pay with my debit/credit card all across Europe, and the same is true for each other EU country. And I still enjoy all of the aforementioned protections and services. So despite the EU consisting of 27 separate member states, with their own banking systems, we still managed to standardize those banking systems enough to offer all of these services across the continent.