I think that we can all agree that the New York Times & Washington Post operate fake news sites. But that does not mean that it would be Constitutional to shut them down. There are many people, who despite the mountain of evidence that they are fake news sites, would draw the wrong conclusion from shutting them down, even if the Court's would allow it.
The only remedy is to arm other sites with the evidence against the integrity of such fake news sites, and launch a major campaign to expose the flagrant dishonesty of such fake news sites.