Is Versailles open year round though? I'd imagine so. As a functioning Royal residence, Buckingham Palace is only open to the public for a short spell each summer.
I just don't think people would lose interest in St Paul's, the Houses of Parliamant, Trafalgar Square, Picadilly circus, the tower of London, tower Bridge, and Buckingham palace if those dreadful people were stripped of their titles and moved into a council block in elephant and castle.
England is much bigger than the royals. Just my opinion.