Our constitution is fundamentally undemocratic. Yes, it has some features of a democracy - for example we are 'permitted' to elect just under half of our parliament - but at its core British politics concentrates unaccountable and unlimited power in the hands of a few, at the top.
Charles writes to politicians at the rate of about 1,600 letters every year, imposing his views on political progress. He bears medals he hasn't earned, pinned on his chest by 'mummy.' How irritating is that for soldiers who have fought and been injured in overseas wars, whilst he is out shooting grouse?
If we have a republican democracy, the queen would be free to campaign to be elected president or head of state, and so would every other citizen. We need a written constitution.
We should not have to defer (I certainly don't) to nonentities who have acquired wealth and power by accident of birth. A true republic would be in the hands of the people and there would be a major shift in the balance of power. Heads of state/presidents (whatever you want to call them) can be removed/impeached if they are corrupt. They would be accountable and have to explain what they do, how they earn their wages, what they spend our money on. Who knows what the monarchy spends our money on? I don't.
A republic would not 'own' overseas territories that have nothing remotely to do with the UK, other than they were 'claimed' centuries ago. Many other countries might feel more fondly about the UK if we stopped posturing - we're a tiny group of islands with delusions of grandeur that we no longer have. Tourism wouldn't be affected - all the traditions that we have can still be carried out for tourism and trade benefits. The monarchy could earn the same pay grades as their staff and higher executives, depending on merit, not birth.
There....now I feel so much better 