If the government asks private companies to do that, then that's a violation of 1st amendment, isn't it?

This is the conundrum social media has created. In the past only the press, who were at least semi-responsible, had the ability to spread information on a massive scale. Social media changed that. Now anyone can spread information instantly on a massive scale, and often it is the conspiracy theories and incorrect information that people seek out.

"We were a bit naive: we thought the internet, with the availability of information, would make us all a lot more factual. The fact that people would seek out—kind of a niche of misinformation—we were a bit naive." -- Bill Gates to Oprah, on "AI and the Future of us".