I've had the same discussion with @Uggo Mongo before and everything I say goes in one ear and out the other. @FrothySolutions' concerns are right for once. Ironically, telling a website owner that they can't control what gets published on their own website would be a violation of their own First Amendment rights.
First of all, there is no First Amendment right to post anything you want on social media. If you consider yourself to be a conservative, and you believe in originalist jurisprudence, that is the natural conclusion you would have to arrive at.
The First Amendment says,
The First Amendment doesn't say you have a positive right to freedom of speech, it only says that you have a negative right in that Congress, (and, by extension, other parts of the federal government) can't deny you your right to freedom of speech. And after Gitlow v. New York (1924), the free speech clause was incorporated to state and local governments through the Fourteenth Amendment.
But social media companies aren't state actors. They aren't parts of, and do not act on behalf of, any government. So it's not a First Amendment violation for you to get banned from Twitter.
Second off, with social media companies, we -- as in the general public -- aren't customers. Advertisers are. There is no antitrust issue concerning social media companies as far as deplatforming is concerned (I mean, there is no antitrust issue when you have no economic relationship with the party in question), and there is no issue with companies attaching terms and conditions to a service, especially one they are offering free of charge. Companies having large market share don't necessarily mean they are anti-competitive -- why, do you guys want to turn Coke and Pepsi into public utilities as well?
Public utilities are regulated either because they are essential or because there are little or no alternatives to it (or nearly impossible to set one up). That's not the case for social media platforms; you don't have to have a Facebook or Twitter account. You don't need a social media platform that respects the First Amendment in its entirety to participate in society. And you can set up alternatives to them -- which is what our forum is when r/incels got shut down, which is what Parler and Gab are. Not that Parler and Gab are free speech platforms; they have pretty strict content policies of their own, far stricter than the First Amendment requires. The only reason they're unpopular isn't that there is "collusion", but because they're a haven for far-right nutjobs who everyone else simply wants to ignore.
Add to the fact that the United States isn't the only country in the world, and that if social media were treated as public utilities, there'd be a whole bunch of cross-border regulatory, privacy, and civil liberties issues. Do American standards apply everywhere? Are Americans, then, allowed to use platforms hosted outside the U.S.?
I wonder if you guys think that a large shopping mall would be obligated to let protestors stage a protest right inside and tape posters everywhere, since it's a public square and protestors have First Amendment rights too, no? Even if their mere presence is deterring everyone else from shopping?
The "spirit" of the law isn't what matters, its the regulatory consequences of it. And this is pretty badly thought out.
Is it bad that a handful of billionaires get to shape public discourse? Yes, but they're not infringing on anyone else's rights, and preventing them from doing so would be a violation of their own rights. What would be legal -- if you are so concerned about the undemocratic nature of Silicon Valley shaping public policy -- would be to have the United States government set up its own social media platform, propped up by taxpayers, run by an independent agency like the USPS is run. Then that platform would have to oblige by the First Amendment.