They don't have to be, many countries in the Commonwealth don't have her as their head of state.

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... I am surprised at your insolence in writing to me at all. You know, as I know, that I bought this constituency... may God's curse light upon you and may it make your women as open and as free to the excise officers as your wives and daughters have always been to me while I have represented your scoundrel corporation.
I have the honour to be... your obliged humble servant, Anthony Henley
- MPs reply to constituent, mid 1700s