Maybe it should. There are plenty of similar laws (e.g. when you sell shares to your 2001st investor you're suddenly subject to a much stricter disclosure regime, and this is widely considered a good thing).
All aspects of a capitalist socioeconomic system exist on the people's, via Congress', sufferance. The very land on which you stand is - at the end of the day - the territory of some government (unless you live in international waters, in space, or in Bir Tawil), and said government carves off subsets of that land for its people to use as they see fit.
Fortunately, we the people here in the US have already long decided that "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances." Those rights are not conditional on whether an entity is an individual person or a limited-liability corporation or an anarcho-syndicalist commune or what have you.
To me the big glaring central point here is that everyone uses big tech platforms. It’s just a fact of life. If you tell people, sorry, I don’t use Facebook, I use some wonky alternative instead, can you add me there? you’ll get weird looks. I think it’s insane to just ignore that elephant and continue studiously down the path of, well, they’re a private company and therefore are entitled to publish whatever they want.
When we established the precedent that private entities can say what they want, we clearly didn’t have Facebook in mind. Like there is just intuitively an obvious difference between a private journal deciding what to write about and a huge platform everyone uses deciding what to pass through or not. The state of the law doesn’t currently reflect this but that doesn’t mean the difference doesn’t exist.
The actual right you have is spelled out in the Constitution: that Congress shall make no law abridging your freedom of speech. That's all you get. Thankfully, the framers did not add a law granting you the right to force me to amplify your speech with my own resources.
Get a blog! The very worst people on Earth have managed to keep blogs running.
This really seems like a case where the existing categories in the law created hundreds of years ago are no longer adequate to capture present realities, similar to how they didn't have AR-15s in mind when they wrote 2A. If you ask whether Reddit is a public or private company, sure, it's private. But if you look at what intuitions back then were around "public" and "private", and for that matter around what "speech" was, it seems like the real answer is that (in regards to this debate) Reddit is a third type of thing that doesn't have a name yet.
> Get a blog! The very worst people on Earth have managed to keep blogs running.
This might illustrate my point better. I assume you don't support people getting banned straight off the internet. Is it simply because no one owns the internet, but Reddit is owned by Reddit (the company)? Maybe it's time for that boundary to be reexamined.