every country has to have some sort of state figurehead.
Genuine question: Why?
Why could we not have a codified written constitution, enshrined in law and backed by the Supreme Court, to which we all owe our allegiance and to which all citizens are subject, even (especially!) the Government of the day?
If we wanted a flesh and blood figurehead to go round opening hospitals and greeting foreign dignitaries then that could just as well be served by making it a voluntary position with a fixed term of one year for which ordinary citizens could apply and be chosen by lot.
Granted the Queer old Dean has done a spiffing job of playing the role for 70 years, but it has to be said she's a bit exceptional in that regard, it's not like the Royal Fam has been exactly awash with decent folk since Victoria.
