Dubious as in you don't agree with them I assume? I found two that said they brought in more than they cost. They weren't hard to find, sure some we be slanted to say they don't. But we are where we are , I don't think they are as popular as they were , but the King and Will and Kate are very popular. Always get lots of support, with only a few protests.
No - dubious, as in they don't stand up to more than a cursory reading. As I said, they include things that they are custodians of on behalf of the state (which should be the people), but still keep huge amounts of money that they generate. They also attribute masses of tourist income, which wouldn't go away if they had less money, and may well increase if their properties were more open.
I don't doubt they're popular, but as my comment said, we'd get the same benefits if we ensured they were just very rich, rather than unimaginably wealthy.