Were you offered to vote for Von Der Layen by the way?
The chancellor in Germany is also not directly elected by majority vote but by parliament.
Its a reasonable criticism that the EU structures make democratic legitimisation very indirect, but that is at least partly a result of the EU being a club of sovereign democracies. The central tension was extremely evident during the Greek debt crisis, you have a change in government in Greece, but due to EU level constraints they can't enact a change in policy. More independent power ininstitutions less dependent on the member state, means the sovereign democratic national governments can't act on their local democratic mandates.
Except the are a couple degrees of separation between the democracy part and in the running the EU institutions.
The EU parliament is also a very superficial imitation of a real parliament in a democratic state. It has very limited say in forming the “government” or decision making.
> result of the EU being a club of sovereign democracies
So either revert to it just being a trade union or implement fully democratic federal institutions. The in between isn’t really working that well.
The parliament would have picked Weber, but nobody cared since its just there to rubber stamp predetermined decisions.
He was the leader of the party which won the plurality in the elections and had its support. EU had a real chance to move towards becoming a real parliamentary democracy if it went that way.