I'm not following on this too closely.
Is this the government asking for social media companies to implement and execute on their own TOS? I'm not a lawyer but it may not trigger First Amendment protections. Nobody is inherently entitled to free speech anywhere at all times. You're not entitled to protest on private property. Isn't social media space online basically the same thing? In my mind, the government asking companies to police their platforms is not the same as prosecuting individuals for what they've said. The latter is the protection offered by the First Amendment.
That said,
I think a revision or re-interpretation of the First Amendment of sorts is needed to govern social media platforms. Some sort of online public square provision so that people can have their speech protected on these platforms. Entrusting policing to corporations is going end badly either way.