Actually, that is exactly how this country works. He’s not asking for the government to step in and take over. Boycotts have always been a way to make a difference in businesses that are doing harmful things. They were a major factor in turning around the Jim Crow South during the 60s. Companies have always use their dollars to make change because in a capitalist society, that’s where the power lies.
If CNN or any other station, liberal or conservative or otherwise, was seriously spreading “fake news,“ you would be fully within your rights to push for advertisers to pull their money. But the truth is, outside of Russia and North Korea, there is no other outlet like Fox News when it comes to truly spreading false information and propaganda. (Although, OAN is probably up there.)