This story first came out a few years ago, where Charles was talking about it being a public and government centre for visiting diplomats and conferences etc.http://www.dailymail.co.u...m-Palace-turn-museum.html
I don't think he has much affection for it and unlike his siblings hasn't lived their for some time (I'm not sure if he left when he married or before whereas they all still keep their London apartments there) Neither William or Harry have ever lived their so I guess they have even less connection to the place.
Its not historically an important place for the monarchy. Officially St James' Palace is the royal seat and HQ not BP.
They could keep using BP as a centrepiece for the big royal occasions with balcony appearances, garden parties and investitures etc, while he can stay at Clarence House (which is part of the SJP complex and somewhere he's invested quite a lot of effort and money into jazzing up) and Windsor. I'd agree that they are Palace heavy in London having BP, SJP/CH and KP all in use. KP might stay with an ever reducing presence as the old guard disappear, so in the grand shake up, it might be that KP will go eventually
Taking out BP also removes quite a chunk of real estate from the royal accounts, so it would be up to the government to maintain it under this plan and not taken from the sovereign grant.