There are many nationally disgraced politicians seating in the EP, EC or council. Only the ones in the EP were electible.
The people have correctly identified that a massive supranational unaccountable government is the problem, enabling corrupt people to keep ruling which undermines the core functioning of representative democracy.
Not terribly different from how prime ministers ate appointed.
So, even if they might not be explicitly elected to be in the EU governance, most of them have reached that spot through more or less democratic means. "More or less" because Prime Ministers are usually nominated not elected, but that's still as part of each country's democratic process.
It lately became en vogue to deny the problem completely and EU politics only got dumber from that.
If I see any issue with the way EU passes laws is with the terrible overhead of having three to four bodies that govern the whole process, from proposal to legislature, not necessarily with the way some participants get there.
Representative democracy works better with increased locality, where policy and politicians are directly beholden to constituents.
