Nope. Dollars and euros can be held in physical form as paper bills and metal coins. No bank is required for that.
Yes, that would be a decentralized exchange, albeit a rather cumbersome one.
"Decentralized" doesn't mean "zero-risk". Whether it's cumbersome or imperfect is immaterial. Using paper bills and metal coins is the only way to implement a fiat-to-crypto/crypto-to-fiat decentralized exchange because it's the only fiat payment method that eliminates the need for an intermediary, avoids counter party risk, and is the one that is most difficult to reverse. Any fiat payment method involving a financial institution is by definition centralized.