Note that the US has a specific mechanism to address this disconnect. Anyone who exercises any real power and discretion in the executive branch must be appointed by the President and confirmed by the Senate. The executive bureaucracy may be sprawling, but you can lay the blame for any significant policy failing directly on someone you voted for (or against).
Which is about the equal to the EU. Council of the EU [1] has similar function as the senate in the US. The council is made up of the heads of governments, as elected, by the member countries. The council proposes the commission, which is then left for the EU parliament to confirm.
This very close, pretty much about equal to the election process of the US senate before the 17th amendment in 1912.[2] The difference being no popular vote for the president. As is the case for the "head of state" for pretty much all European countries. Exceptions are only France?
The major difference is that only the commission has the right to legislative initiative. To balance this the EU parliament can dissolve the commission based on a vote of no confidence.
So all in all, it's a truly democratic system with all the checks and balances. The major difference is the lack of cross European parties, thus your choice becomes collected together in the same basket as what your chosen party thinks is the right path. Completely through representative democracy, either from the head of government or European parliament.
Not many Americans realize that the original vision and the implementation of the political organization of the United Stated was very resembling that of European Union. The US states were just a bit less sovereign than EU member states (with differences mostly about having independent militaries and foreign relations), and the role of the federal US government was closer to what role EU plays for its member states.
Then, suddenly, in early 20th century, the federal US government made a huge power grab, and now the states are mostly just subjects of it, with much less sovereignty remaining. That’s what some EU skeptics are concerned about as well: sudden sweep and becoming subjects of Brussels.
