Actually European integration the last 30 years has been pretty remarkable. In the past, not even electric plugs were compatible. But the EU is not a country. A lot of the inefficiencies are actually features sought by key members to protect their own local incumbents.
Money transfers between bank accounts for no extra fees (well, that's limited to the Euro, so a couple of countries chose to stay outside). Mobile phone usage for no extra fees all over EU (some limitations, but typically not relevant for the average trip).
B2B the integration has even bigger impact.
I don't think eletric plugs are even regulated. British plugs never changed and they were not an argument in Brexit.
My bank requires me to fill in a paper form, scan it, send it by mail, wait a week, then get an answer (often, "no, give us more details") if I want to send money in another country. Neobanks tried to solve this for lower amounts, but will freeze easily your account for "AML" if you send low six figures.
And many non eu don't have. I am neutral on the eu topic but you are confused. If this eu thing can mandate certain water standards or expel a country and or withhold common funds, that's a very different thing from seeing "some" non eu countries having water.
