It used to be that they didn't moderate content themselves for fear of losing their "common carrier" protection.Reddit allowed porn from the beginning. Facebook never allowed nudity. Neither one of them had any common carrier protections to protect or to lose by these policies.
Reddit proves that even subreddits, personal filters, and other self-moderation tools are not enough to prevent politician, media, and advertiser pressure around controversial content. The jailbait subreddit, like every subreddit that has been banned, was full of willing subscribers.
I can't name any prominent American politicians who really want social media to publish everything that's allowed under the First Amendment. Do you know of any?
Some politicians say that they do but I don't believe they have considered the full scope of what is actually allowed under the First Amendment. For example, Senator Tom Cotton published an apparently fierce defense of free speech on his own web site in June 2020:
https://www.cotton.senate.gov/news/op-eds/twitter-tried-to-c...
It ends with
These social-media companies have improved the lives of Americans in many ways. But they should not be surprised public opinion is turning against them when they act as censors and moral scolds to millions of Americans. Nor should they expect to find many people rushing to their defense. In fact, to coin a phrase, those of us in their crosshairs might say: No quarter for Big Tech censorship.
However, in September 2020 he accused Netflix of distributing child pornography (the movie Cuties) and wrote:
Netflix has a basic legal responsibility to not stream child pornography or otherwise promote the sexual exploitation of children.
https://www.foxnews.com/opinion/netflix-cuties-child-pornogr...
I don't think that he understands how broad the First Amendment actually is, and how narrow the exceptions for obscenity and child pornography are. He just wants to make tech companies stop censoring his tweets and start censoring movies. Likewise, many activists who are upset about (e.g.) LGBTQ content getting suppressed by YouTube algorithms don't much care about YouTube suppressing videos about guns and explosives.
There are few people except perhaps Constitutional scholars willing to defend the full breadth of what the First Amendment guards, much less require social networks to host content of similar breadth. I'm willing to defend the First Amendment as it currently exists, even the publications I find vilest, but I don't want social media forced to publish all of it.