I don't support the monarchy but that's for another thread.
As far as the repairs to Buckingham Palace are concerned, I think the either of the following should happen.
Choice A: Buckingham Palace could be declared to be a public building. A small appartment within it would then be reserved for the Windsors to live in, and it would never be open to the public. A larger portion, possibly part of a wing, would be open to the public when not needed for state functions. Most of it would be open to the public all the time for an entrance fee. The state would pick up the tab for maintaining the entire building, offset by income from visitors.
Choice B: Buckingham Palace continues to be largely set aside for the use of the Windsors. When major rennovations are needed (as they clearly are now), it's the responsibility of the Windsors to draw on their very considerable incomes to fund it.