For an even better example, see India where the poorer states get very large subsidies and investments and quite a few have had substantial quality of life improvements over the years. People argue that Europe can't have a union because of its diversity but India is far more diverse in terms of languages, culture, religion and politics and has still managed to forge a nation atate.
In Europe, the rich countries essentially keep their own taxes and don't transfer and invest taxes in the poorer ones, so being tied to a strong currency trips up the poorer states badly - all the disadvantages of being a weaker area tied to a strong currency without any mitigation factors beyond the right to move away.