Instead of a "Single" currency, there should be a "Common" currency (with notes and coins) available to be used in all EU states and whose value was not allowed to devalue against any of its constituent basket of EU currencies, i.e. the inflation rate of the "Common" currency would always be equal to the lowest inflation rate of the currencies that made it up. That would encourage people to hold and use it and over time people would migrate to it. It would also allow businesses to only concern themselves with a single exchange rate, namely that between their national currency and the Euro Common currency.
The UK suggestion was, of course, rejected out of hand.
The EU is about a forcing the creation of a single state.
It is a political project rather than a practical one.
Hence Brexit.