The license fee has been criticised because it forces people to pay money to the BBC despite it not accounting for the majority of TV. But those in favour of the fee fear for the future of the BBC if the fee is scrapped.
In particular, proponents of the fee worry that the quality of the content will suffer.
The license fee allows the BBC to fund its programming without being limited advertisers. With public funding, the BBC has full control over its content and has the power to choose how to spend their money. For example, David Attenborough's Planet Earth has cost more than £16 million and Downton Abbey cost more than £1 million per episode. 
Few funded channels can afford to spend so much even if the content is of extremely high quality.
It's true, the BBC is not watched by everyone, but it is designed to benefit everyone. Because they rely on public funding, its content remains independent from private corporate influence.
The license fee ensure that remains in the hands of the public, ensuring that the power remains with the people and free of outside influence. This ensures top quality independent content for all.