This is an asset of state
I can only say his letter appears to lack research and be based on his own prejudice. If he looked to the fullfact.org.website, he could have enlightened himself as to the fact that the Queen is funding the renovations.
The Queen does not own Buckingham Palace, it comes with the job. Do other occupants of residential property linked to a job pay for renovations?
It should also be understood this is a property to be enjoyed by visitors. The Palace is used to receive visiting Heads of State, it hosts state and ceremonial occasions and has members of the public touring the State Rooms.
It is truly an asset of the State and should be funded as such.