This would mean that all media companies in the US would be prevented from publishing anything that could be perceived as negative about any candidate running for elected office, regardless of factual basis and regardless of if it were satire.

A candidate would simply go to any circuit court judge and get an injunction against the media company. If the media company did not comply, the judge would find the officers in contempt. Marshals would then arrest and throw the companies officers in jail indefinitely until they complied.

That's what you're asking for. It's genuinely stupid. I say this as someone that would declare a national emergency on day 1 of being elected just to have the Air Force turn most media company HQs into smoldering craters.