It's tradition, looks nice and just gives us something to forget about our own woes I suppose. Yes there is the argument that they bring in money through tourism and they do but that usually just goes back into keeping them I don't think the economy would suddenly crumble if we got rid of them because the money lost from lack of royalist tourists would be made up on lack of money spent on them. The whole tourism thing just seems like a smoke screen just to justify the fact we really just have them because we simply like them. Most people come to London go to the London eye, big ben etc.. anyway.
Having said that I do quite like having a royal family as long as we don't give them too many handouts like a state funded boat (stares at Gove) and the cost of keeping them doesn't exceed the amount we get for tourism. Besides what would we do with them if we suddenly decided we didn't want them anymore? I don't think the EU will be too happy with beheading them.