Say what you like about the BBC -- as indeed you are doing
-- but, if you are serious about the money that is spent on your behalf, you can see the BBC's accounts any time you like. They have to be published under the public accountability terms of the Royal Charter. A consolidated form of them is published as the
BBC Annual Report, which you can easily find online. It will swiftly become clear than the so-called "huge fees" to headline performers are chicken feed in the overall scheme of things.
They are also well below the fees paid by the commercial broadcasters, by the way, for which we also pay! It's less obvious because the advertising revenue that funds those channels is part of the price we pay for goods and services in the shops.