Why do you think ‘it’s the finest system of government ever devised?’
I'm not a royalist nor a republican and wouldn't say that at all but I'm happy enough with the current system.
It will a huge upheaval to get rid - according to consitutional experts I've seen not be easy to do as there a space for a head of state and it's not always as clear who owns what - so it would take time money and poltcial capital for what exactly what the next step look like.
We've just had brexit with no clear end goal and that's cost us economcially and brought no obvious benefits yet. Looking round the globe constitutional mochanies seem a fairly stable system compared to many other type of government.
This country has been a republic - after brutal civial war - and we ended up with a Lord Protector who disbanded parliment - so had less control over him that previous King we'd just got rid of and tried to pass position on to his eldest son.
France went from kings to mass killing, civial war to French emperors brief flirt with a king with The Bourbon Restoration to modern government - hardly plain sailing involving huge debts and lots of death.
We've spent centuries stripping power from our Monarchs they have some still but image we'll continue on current path of dimishing their importance and using them where we can. At some point family might want not to do it any more and it woudl be mcuh easier to get rid at that point.
If you want to sell me on a republic now tell me exactly what you want instead and how much it's going to cost and what the benefits are to me and the rest of us voters.