I'm not a big fan at all of the EU but I think your statement "The EU is governed by the commission et al and they are not elected." is a little misleading in that they are nominated by member countries and there is some sort of voting/approval by the MEPS amd /ability to dismiss but I'd agree that in practice it seems to have a pretty free rein.
From WIkipedia:
"While the commission is the executive branch, the candidates are chosen individually by the 28 national governments, which means it is not possible for a commission member or president to be removed by a direct election. Rather, the legitimacy of the commission is mainly drawn from the vote of approval that is required from the European Parliament, along with its power to dismiss the body, which, in turn, raises the concern of the relatively low turnout (less than 50%) in elections for the European Parliament since 1999. While that figure may be higher than that of some national elections, including the off-year elections of the United States Congress, the fact that there are no elections for the position of commission president calls the position's legitimacy into question in the eyes of some.[84] The fact that the commission can directly decide (albeit with oversight from specially formed 'comitology committees') on the shape and character of implementing legislation further raises concerns about democratic legitimacy.[85]