Basically, other countries can bank in USD sometimes, so there's a weird corner case that you can send USD to a merchant but can land in their account as $converted_currency or USD that isn't so corner. I'll let patio11 cover this (if/when he gets to it) as there are details I no longer have access to and thus can't do the subject justice.
If you choose USD, then the merchant gets to choose whatever exchange rate they want to convert at, and will be far from the spot price (hence some merchants go out of their way to ask you if you want to pay with USD). If you choose the local currency, then your American bank will give you an exchange rate extremely close to the spot rate and the transaction ends up being much cheaper for you.
Once you start investigating, you will find many different reasons. Some cultures favor cash because it's concrete, or for privacy reasons. In some countries, banks prioritized efficiency and were quick to phase out checks in favor of wire transfers. In many cases, stores were used to cheap domestic payment methods and didn't start accepting international credit cards until banks made them cheap enough. And in some cultures, there is a deep aversion to anything related to debt. If you dig further, many of the reasons can be traced back to adverse experiences in the 20th century, including world wars, the hard times after them, hyperinflation, and living under nazi/communist rule.
this applies only to a subset of Europe or european banks.
Instant transfers may cost fees
Europe is bigger than EU.