The people who try to support the Windsors as our head of state have no logical case to offer. So they spout the nebulous concept that tourists come here because of the Queen. This is patently absurd. London has vastly more attractions for a tourist than the monarch. And, in fact, without the monarch we could accommodate far more visitors to the royal palaces each year.
Buckingham Palace, Windsor Castle and other residences including the Palace of Holyrood house in Edinburgh and Clarence House all combined have 2.58 million visitors who pay £55 million for the privilege. Remember that this is the TURNOVER not the PROFIT, so the contribution made to running the monarchy will be a small fraction of this. In fact the Royal Collection Trust paid just £4.4 million to the Royal Household in the latest figures. Compare and contrast this with the £300 million a year it costs to run the royal family and you can see that it is insignificant.
In France they made the sensible move of getting rid of an unelected head of state some time ago. This means that the former royal palaces and their art collections are available to visitors all year round. So the Louvre has about 10 million visitors a year and Versailles about 5 million. There is also the Palace of Fontainebleau with smaller numbers. Then there are the Jardin du Luxembourg and Jardins des Tuileries, which must attract even more. The Palais-Royal is used as government offices and the Palais de la Cité as law courts, so France has the potential to earn even more from royal tourism.
So there you have it, if you want to earn more tourist income from the royal family then you need to get rid of them.