I happen to live in the EU so I may have a slight clue what I'm talking about.
But if you want an authority on the subject, look up Yanis Varoufakis and how sovereignty and democracy worked out for Greece when shit hit the fan.
Europe was able to impose policies to Greece because Greece was requesting loans from Europe. Those loans were required because other investors were unhappy that Greece had hidden the real state of its finance in its reports.
Greece took on more debt than they could serve. Do you expect the tax payers from other countries to just pay for that without significant changes to how Greece operates? If you can't pay your debts and you can't print your own currency, you lose some sovereignty. But I feel like Greece would have been worse off if they still had the drachma and tried to print their way out of the crisis.