Ok, I can see where you are coming from, but I guess we fundamentally disagree on this. I see any company that provides a de facto public "square" as being equivalent on some level to a public space. (Much as malls were deemed to be a form of public space in the courts a while back, not that it is completely settled law.)
In my opinion, when a company's platform becomes one of the largest and most important venues for public discussion, they can no longer be considered a purely "private" entity in the same way. Corporations exist at the leisure of the public, as the public allows their charters to exist and defines (through law) the powers granted to the corporation. Expression of fundamental freedoms like freedom of speech defeats corporate concerns in this case. The public square must be open to the public, or democracy cannot function.
There are two key differences between Twitter and public space. One is that public space is owned by the public. The other is that public space is physically central to a community. All web sites are equidistant. The reason we don't have public space on the Internet yet is that we have a such a superfluity of private spaces.
I get your theory that private community spaces take on additional responsibilities once they're important enough to a community and maybe there's a way to legislate that. But it would be challenging. HN is definitely an important space for this community, for example. Every local newspaper is important too. The notion that we should have detailed federal regulations for exactly how to moderate a discussion thread plus a legal appeals process strikes me as unworkable in practice.
If we really want virtual public space, I think the thing to do is just to build or buy it. It would be easy enough to nationalize Facebook and Twitter for example; Congress just says "now they're part of the government", optionally paying the shareholders.
"Public" and "private" spaces are not so clear-cut. Not all public space is publicly owned. Again, see the shopping mall: https://www.minnpost.com/cityscape/2015/03/complex-role-mall.... As the article points out, the notion of "public space" is really a sort of conflict zone with ever-shifting boundaries. (If you remember "free speech zones" you can see how even fully public space gets attacked when protest becomes inconvenient.)
I completely agree that it would be impractical to legislate moderation or terms of service, except on maybe a very coarse scale. I'm not sure what the answer is. Like much in the political sphere, this may just be a space where law and litigation has to fight it out with private industry until the end of time. A "solution" that satisfies all parties may not be possible.
In my opinion, when a company's platform becomes one of the largest and most important venues for public discussion, they can no longer be considered a purely "private" entity in the same way. Corporations exist at the leisure of the public, as the public allows their charters to exist and defines (through law) the powers granted to the corporation. Expression of fundamental freedoms like freedom of speech defeats corporate concerns in this case. The public square must be open to the public, or democracy cannot function.