Prior to the adoption of the euro, the Danish crown was pegged to the D-mark (since about the mid-1980s), because Germany was the biggest export market for Denmark (still is), and thus having a currency that's stable towards what the Germans are using has been good for Danish exports (less sure how relevant that still is). (Sidebar; had the original motivation of Alternative für Deutschland been successful and abandoned the Euro for a return to the D-mark (neumark?), it would have put Denmark in an awkward position.)
The last time I was in Denmark my bank nicely charged me for the conversion despite the coin being fixed to the euro. It is just a money costing machine which adds no value.
Ask Greeks how much they enjoyed ECB involvement.
Germany even without any representation in ECB will have much more to say than other countries. Because in the end it is a real political power that allows anyone to make decisions.