One core value that a platform could have is common decency, which is not the same as censorship, but it is given up even easier than what your argument calls free speech.
How do you suggest making a platform which allows good content while disallowing bad? Also, how do you expect to be able to define these things? Remember: every person you pay to moderate has to be able to discern good from bad in as little time as possible. Even less time than that.
I have no idea how to apply this to a content hosting paradigm though. Not without spending a couple million dollars on bots who inevitably make mistakes.
I suspect you'll find out that whatever free speech rights your local jurisdiction grants you don't allow you to stay in the bar.
Since somebody downvoted without providing references to their refutes here's an actual case about freedom of speech online which is the main one by the looks of it in regards to suppressing speech online:
https://en.wikipedia.org/wiki/Reno_v._American_Civil_Liberti...
The burden of defamation is on the person not the website if anything, however, if someone posts anonymously who do you sue? The best a platform can do is delete their account. I've successfully had defamatory / false content about myself deleted from a platform in the past.
If someone wants to argue that YouTube should be declared a public utility that is required to host everyone’s content no matter what, that’s totally understandable and they should make that argument instead. Otherwise they’re just asking for the government to mandate that YouTube, etc. are safe spaces where everything is permitted and no one is allowed to judge other people for what they say, including the company paying for the servers. Which is so totally counter to what those very same people seem to think about everything else that I’m surprised the hypocrisy and inconsistency doesn’t create a singularity or something. But here we are, in 2020, and AM-talk-radio types are demanding the government mandate safe spaces for them on privately owned platforms where they are shielded from consequences.