Earlier quoted context omitted.
They are not irrelevant in the sense that they are a declaration of the nation that there are special people by birth. In a society so worried about equality, it is appaling that multiple countries in europe not only have populations that leave under monarchy, but that they seem to be in favor.
None of that monarchs is involved in actual legislative, executive or judicative activities. Sure, they are heads of state, but that's where it stops. European monarchs don't write laws, don't sign laws, are not part of the elected government.
At least in Norway, laws have to be signed by the King and the prime minister (with a few exceptions); for example, in 1975 the King did not sign a law passed by Parliament/Stortinget and the law did not become effective (this was, however, a special occation related to a strike where the two parts found an aggreement after the law was passed by Parliament but before it was signed by the King and the prime minister, so the government recommended the King not to sign). See https://lovdata-no.translate.goog/artikkel/vil_kongen_nekte_...