To clarify 1 point, it is true to say that the Monarch has no direct control over what is currently part of the Crown Estate. What they do have control over is what remains outside of that public control.
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That - does not make sense
The Monarch has no control over the Crown Estate
If, for example, the Crown Estate wanted to add Balmoral to their holdings they would have to buy it from the Monarch
It's true that they probably wouldn't agree to sell it - but why would the Crown Estate ever want to buy it?
There's a whole bunch of expensive property that costs the Crown Estate tonnes of money and doesn't provide a revenue
The Crown Estate makes a billion pounds profit a year - it doesn't do that by buying even more unprofitable property
So even if the Monarch wanted to be able to sell Balmoral to them - they wouldn't agree to buy it
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To quote the article you provided, "The Sovereign Grant is drawn from Public Funds"...
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Technically the Sovereign Grant is all paid out by general taxation
But (using the new figures) - the Crown Estate gives the government 100% of it's money
The government gives the Monarch money equal to 20% of what they have received from the Crown Estate
Doesn't that seem a lot like the King is paying 80% tax on all his "public" property
And Occupied Royal Residences - which Buckingham Palace is because it is the administrative headquarters of the Monarchy even if no one lives there - are parts of.the Crown Estate which are the responsibility of the monarch
Which is worse - for the Monarch
If they had any say they would leave that as a liability for the Crown Estate - because then they wouldn't have to pay for it
The government made the extra money available because this is the administrative H.Q. of the Head of State - so mildly important
But that was all a percentage of the money that was originally taken from the Crown Estate to start with
The article you posted has very little in common with what you have been saying
You seem to be mainly talking about the Crown Estate but referring to their private finances - which is a completely different topic
If you were interested in the Crown Estate finances they publish them every year in their annual report - you can get it here
https://www.thecrownestate.co.uk/about-us/annual-report