The answer is that figurehead is actually a very important office. It is from the crown that the British government obtains its claim to legitimacy . The source of legitimacy is not always be the same as the effective authority in civil government. In Britain legitimacy is invested in the crown, and governing authority in the Prime minister and House of Commons. The government is theoretically subject to the crown.
Legitimacy is indespensible.
Legitimacy is the difference between a State and an organized crime syndicate. I can confidently predict that, as irrelevant as the monarchy is to actual British government, and as unworthy is the conduct of most of that royal family, Britain would become ungovernable if the monarchy were abolished. It does not help The tabloid-style lives which most of the royal family lead, may severely strain their legitimacy after Queen Elizabeth dies. The United States faces similar problems. The growing perception that the judiciary will take all the big decisions, that elections are rigged, and that the elected officials are corrupt, and that actual governing authority has gone to an unelected bureaucracy, has sown doubt in the minds of the people.