[0]: https://www.statista.com/statistics/991925/visitors-palace-o...
[1]: https://www.statista.com/statistics/373081/uk-royal-tourism-...
These are not the sorts of places that people typically visit on overseas holidays more than once. So once the ticket has been bought, whether or not it is "an actual royal palace" is irrelevant.
Of course people like to feel the glamour of being close to the mystique of living wealth, but once an attraction is firmly on the circuit it hardly matters. See Tower of London, Blenheim Palace, Edinburgh Castle, Hampton Court Palace, etc.
According to Association of Leading Visitor Attractions, Buckingham Palace would be around the 70th most visited attraction in the country, hardly a sign that you need a living monarchy to sustain tourism - https://www.alva.org.uk/details.cfm?p=423