>Not really. There's a certain political party who seems to want to redefine private companies as public commons, all because they don't like their hate speech being censored.

no, it's because it actually became the new public commons. That's where most gets their news, meet people, organise events, find jobs, etc. Politicians and organisations are now using it as their main mean of communication.

How do you think the 2020 election would have gone if twitter + facebook + reddit decided after 2016 that most anti-trump posts should be removed from the platforms for misinformation and instead they promoted anti-Biden content? I think they could easily have made him won by a landslide

The main gripe isn't that hate speech is being censored, although personally I don't think it should be. We complain about Twitter because anything to the right of Stalin is a potential censorship target, depending on Twitter's editorial marching orders for the day.

edit: I'm a little disappointed in myself for thoughtlessly going along with your framing. There's no such thing as "hate speech".