My post was meant to be more rhetorical in nature, to demonstrate that overzealous censorship is not an issue which can be solved by simply stating "force all non-illegal content to be/remain published".
It's easy to hand-wave it to the courts, but there are many issues with that approach as well (e.g. non-technically competent people making decisions about technology, government not immune to corruption nor censorship, courts are slow by nature).
Your answer also conveniently side-steps the nitty-gritty implementation issues. How does a platform deal with spam posts if they are unable to delete content that is legal? If you don't like a website, simply post a few thousand Viagra advertisements to their front page for a few weeks and they either have to advertise Viagra or shutdown.
Speaking of advertising, why bother pay for ad-space on a website like Reddit, when I can just spam my product on every subreddit over and over again and they have no choice but to keep it up?
Will these rules also be applicable to other forms of media which also have a viewership above the arbitrary "large" line? Newspaper, books, TV? If not, why not?
These are just a few off-the-cuff issues that come to mind. I'm sure people smarter than me who take some time to seriously consider this approach will be able to find hundreds of such examples of why "forced to publish all non-illegal content" sounds great but is simply not a feasible solution to the problem.
As an aside, I find it odd that the answer to censorship by private companies is to offload everything to the largest centralized system with the longest history of censorship: governments.