Yes, so where can I store USD / Euro without being verified?
Basically every single exchange that accepts tether deposits and withdrawals. Obviously if you consider tether to be a valid form of USD anyways. But bitfinex does allow you to store USD with them without verification(they are heavily involved in tether, however).
Also, on kraken you are able to trade fiat currencies and store fiat currencies as long as you are tier 1 verified. And tier 1 pretty much is going to be just providing a name and a country, there isn't really that much substance involved.
Storing fiat on exchanges are definitely not the best way to do it. You're getting no interest, but still carrying the risk of the exchange collapsing.
I don't trust tether atm.