Why Isn't the BBC's Director-General Elected?

Amid all the controversy over Jonathan Ross and Russell Brand, one thing puzzles me. Why isn't the Director-General of the BBC elected by the license fee payers? After all, the chairman of a company is elected by the shareholders - or at least submits himself to a vote. The board of a charity such as the National Trust is elected. So is the chairman of the local golf club. Why are the people who pay for the BBC not allowed any say in how it is run? The Director General should be elected by the license fee payers, on the basis of one license, one vote. Different candidates should run. Some could be more populist and argue for a higher license fee. Others could argue for a £50 fee and a smaller BBC. It would certainly be amusing seeing anyone trying to defend paying £6 million a year to Jonathan Ross in an open election.