What people are focusing on is the reach of social media. "Because this is where the most people will hear it, it's where my speech needs to be protected." Because there's many other venues for communication other than Twitter. I don't think it qualifies as the town square. Plus, it cuts both ways. Politicians can't block people calling them the worst things imaginable on their social media account? Then vile, racist, borderline calls to violence also can't get censored or blocked, as a similar violation of people's Free Speech.
IMO people are arguing for control of the tech, and not the actual merits of Free Speech. Even though they're adjacent. People want to litigate the rules of a non-public entity because it's where people's eyes happen to be right now, and will be for the foreseeable future unless the Golden Man Child fucks it up even more.
This is why I cringed when Trump really cemented the idea of Twitter as some sort of bedrock communication channel of American politics. Because it's not. We're practicing Free Speech, right here, which is why I imagine the First Amendment sought to protect. People's ability to gather and talk about what they felt like without being subject to arrest. Not "I have the right to talk AT YOU."