The government/private line is useful because it's a very bright, clearly defined line, and also ideologically consistent. It seems to me that saying that to protect free speech, some private entities must be forced to carry speech is a contradiction that actually degrades free speech, rather than protects it. It also moves the question to "Which private individuals must be forced to carry speech?"
You've made an argument that you're too small and insignificant, but that seems to be a matter of opinion to me. How small is too small? Consider a forum for you and your friends. How many friends are allowed on your forum before you are forced to carry any and all content that others wish to post there, and who makes that decision? Will you be forced to let Nazis on your forum? Ads? Porn? Will you be able to moderate anything at all?
Keeping the line at government/private protects Twitter, but it also protects you.
This is a slippery slope argument. Yes, the line becomes harder to define, but we can agree that there is a huge difference between the internet's public square and my small private forum.
If many of the functions that a government fulfills are now implemented by private entities, I want these private entities to inherit the limitations of power we place on governments. Is that ideologically inconsistent?
Maybe under perfect competitive capitalism, this wouldn't be an issue, but unfortunately this is not the world that we live in. I could cite many examples of free speech oriented social media apps that were shut down by their hosting provider, their payment processors, the two app stores, cloudflare, etc. Is it that different from a government shutting down a newspaper or preventing a group of citizens from assembling?
I would much prefer a technological solution rather than more government intervention (perhaps a move towards decentralized censorship-resistant hosting of content), but the first step towards a solution is to recognize that we have a censorship problem, even if the government is not directly censoring anything.
You've made an argument that you're too small and insignificant, but that seems to be a matter of opinion to me. How small is too small? Consider a forum for you and your friends. How many friends are allowed on your forum before you are forced to carry any and all content that others wish to post there, and who makes that decision? Will you be forced to let Nazis on your forum? Ads? Porn? Will you be able to moderate anything at all?
Keeping the line at government/private protects Twitter, but it also protects you.