Surely what people come to see will still be there in a republic?
Probably not.
Yeah, things like the castles will still be there, but the royal family itself generates at least some publicity/interest. And if they were elected, the head of state would be "just another politician".
At least in a republic you can get rid of an incompetent head of state.
True. But in a constitutional monarchy, actual real power rests with elected politicians. Yes, a head of state who's a monarch can be incompetent, but their ability to cause damage is limited.
Plus, some might see it as an advantage to have a head of state who could (in theory) rise above petty politics. (How many people in the U.S. would have preferred anyone other than George Bush to have represented America, even if just symbolically?)
Not only does he talk to flowers, but he's a believer in homoeopathy!
Yup, and the conservative party here in Canada selected a chiropractor as minister of science. (And the liberals weren't much better, selecting a chiropractor as health critic.)
Not to mention all the creationists in various positions in the U.S.
Until the general population of a country becomes more attune to skepticism, there's no guarantee that the elected leaders won't be just as wooish than royalty.