You pay about 10x more for the rest of arts and culture than for monarchy. Presumably people should be able to opt in to that too? Or should the government pay because it is believed to be a social good? In other words--do people have to pay for the rest of it?
If they do, then you have to carefully account for the social benefits and detriments of monarchy as compared to other arts and culture--not that monarchy would necessarily be competitive, but it's only fair to use the same logic.
BBC license fee? What if you prefer Sky? What if you don't want to visit Tate Modern, like, ever? Etc..