In theory the King can veto any law he wants. In practice he couldn't without causing a monumental constitutional crisis that would probably end his reign. His unofficial ability to influence government policy is the real issue, but one that is definitely not limited to that one guy with the special blood.

You can benefit much more as a corrupt politician, as the blame is diluted between the whole government. Single king is responsible for it's actions and we even have a word for throwing them out of the window if they misbehave.

It's much rarer for politicians to even get into jail.

The BBC is monarchist to the core. A lot of people say the BBC is biased in one political direction or another, but they often forget about monarchism.

One notable example of their privilege was when Andrew George MP dared to ask a question in parliament about the Duchy of Cornwall, only to be told he wasn't allowed to. (The Duchy of Cornwall is a kind of slush fund for the heir to throne. Charles had it before he became king. It has tax breaks, and also the ability to seize property and mine on people's land.)