Why are you talking about House, the European Parliament is directly elected as well.

I'm talking about the government, which is a group of nominated ministers (nominated either by a prime minister or a president, and only the later is elected directly).

Take the US for instance: no citizen ever elected Rubio, Bessent, Hegseth, Bondi and co. as members of the Trump cabinet. The US citizens voted Trump, then he appointed them and Senate approved each of them after an individual hearing. That's exactly how it works for the European Commissioners too, except the nomination doesn't come from one president but the European Council, which is made of the 27th heads of states of the EU.

In Australia our cabinet is made up of elected Members of Parliament. They are appointed to their ministry but only our of the pool of elected MPs in the party or coalition with a majority.

Good to know, this is definitely an exception in World's democracies though.

(And if you checked the European Commissioners, most of them have been elected before and a handful were members of the Parliament right before their nomination. They are definitely politicians and not bureaucrats)