That's rather the point though - it isn't "the Royals" that are splashing out on a ceremony, it's the country. By which I mean, he became King the moment that his mother died and doesn't need to have a coronation.I really don't care if the royals splash out on big ceremonies, but I'd far rather they dipped into their own pockets to fund it. It's not as if they cannot afford £100m out of their own coffers, is it?
This is the official investiture of our Head of State, we would likely have some kind of ceremony for a President (cf. the inauguration of the President of the United States).
The advantage of a monarchy is that we only do it once every few decades, rather than every four years.