There is an argument to be made that Fox News should be pulled from the U.S. cable system as well. The cable system, like the airwaves, is owned and regulated by the government. And part of the charter of being allowed to use these resources has been that programming - and especially news - is to serve the public interest. There was an understanding - referenced back to the Founding Fathers - that news performed an essential role in a properly functioning democracy and had on obligation to work for the public interest. Which could only mean that it give reliable reporting.
By calling themselves Fox “News”, they have an obligation to present current events truthfully. An obligation they have never met. They would therefore be in violation of their charter, and could and should be pulled off the air. They could continue their programming if they did not purport to call themselves a news network.