To have a democracy, it requires a demos, or a people who feel attached to one another. Since we are beyond the era of the city-state, when all free citizens could gather on a hillside and vote on important questions, the nation-state is the best way to delineate a people sharing bonds of language, history, culture and institutions.
The 28-nation EU doesn’t have those bonds. It is too big and too sprawling for true accountability. No one in Poland cares how Finland is governed, and vice versa. Forging a Europe-wide government has always been an elite project that necessarily operates outside democratic channels, accruing more authority, mostly out of sight (with an occasional national referendum on treaties, always revoted if it goes the wrong way).
The European Commission, the de facto Cabinet government of the EU, has basically exclusive power to propose European laws. It is appointed and its members aren’t widely known throughout Europe. Once approved by the EU Council (the body on which heads of government sit) and the European Parliament (elected in dismally low-turnout elections), the laws are supreme over enactments by the real parliaments of real countries and can’t be repealed. The same goes for decisions of the European court.