How about tap water has to be drinkable in every EU country

Many non-eu countries have drinkable tap water, not sure how representative of "integration" this rule is.

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.

USB-C!

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.

All of those things don't require having a supranational body who you relinquish large parts of your sovereignty to.

Which is why bank to bank transfers are so easy in the US.

I wouldn't say that transfers are easy in the EU.

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.

Free cellphone roaming is a big plus.