I think this is a good idea. Tourists would flock to Buck house and pay handsomely just to say they have been inside, so a good source of revenue and could be open all year round.We are no longer at Queen Victoria and having nine idle children needing to be housed. Beatrice and Eugenie can find houses in London or wherever they have husbands and jobs. Prince Andrew can be housed in a prison somewhere if there was actual justice in the world. Or shipped off to St Helena. Charlotte and Louis will hopefully have their own lives and live somewhere else rather than all these free houses. There must be somewhere in Cornwall that could take them. All the Royal palaces should be available to the nation. Windsor and Buck Palace included.
Charles's flat would probably consist of about twenty or so rooms but he would only be staying there for business and go back to Highgrove at every available opportunity. The balcony and surrounding rooms would also stay private to be used for the usual Royal occasions.
It works at Windsor while TQ is there so should be no problem at BP.