More importantly, you can’t have a common currency without common economies. How can you marry Germany, which is an industrial export type economy, with Greece, which is largely agriculture and tourism, and the UK, which is now largely a service economy (expecially financial service)? A euro may be theoretically worth the same across the continent, but in fact you can buy far more with a euro in, say, Portugal than you can in, say, the Netherlands.
Or:
A dollar may be theoretically worth the same across the continent, but in fact you can buy far more with a dollar in, say, Georgia than you can in, say, California.