You’re the one who is uninformed; in most (Anglo-sphere) parliamentary systems, the ministers do not need to be in the house of commons (elected), and often do

You’re the one who is uninformed; in most (Anglo-sphere) parliamentary systems, the ministers do not need to be in the house of commons (elected), and often do not even have to be parliamentarians. Lord Halifax was eligible to be prime minister of England, despite being unelected, and Canadian prime ministers who lose their riding usually remain prime minister.