All of the top jobs have nothing to do with democracy.
They sort out who gets what job behind closed doors. We saw this when the current session started.
The electoral college isn't horse-trading behind closed doors. Each congressional district has equal weight in the electoral college.
I'm curious, do you actively promote your country surrendering its sovereignty to the EU? It would save you guys a lot of money if you got rid of your national government and let your beloved EU have direct rule.