Present-day social media censorship in the US is not "just free market", and is markedly similar to the kind I experienced growing up in a now-ex-communist eastern European country in the 1970s-1980s. Outright bans were not politically tenable by then, but forcing the opposition to express their views on fringe "alternative" channels was a popular strategy [1].
WeChat does not let you share Winnie the Pooh. Nominally, Tencent is a privately owned company freely choosing who they provide a platform to [2]. But in reality, they have no choice but to ban Winnie the Pooh, unless they want a state apparatus to make their lives increasingly difficult. Just because something is censored by a private platform doesn't mean that it's the "free market" of ideas and not a state or the government wielding its power.
Large US companies are also part of an industrial–congressional complex, with lobbying and political contributions on one side, political approval and threats of regulation on the other. Large tech companies are deeply and inseparably intertwined with the state and the political parties (both of them), based on the granting of reciprocated privileges. They know full well that if they ban the wrong speech (or refuse to ban the "right" speech), they face being regulated out of existence. Indeed, seeing this threat, we see them scramble to align with the incoming administration.
The kind of social engineering that led to the present bans was very popular in communist Eastern Europe as well. Did you recite an anti-government poem at your barbecue? You might find yourself banned from your favorite pub permanently! Why? Nominally, it was the bartender exercising his right not to serve you: after all, he shouldn't have to suffer potentially vocal ("verbally aggressive") imperialists in the establishment he runs. But behind the nominal reason was plain, state-mandated censorship. They'd have risked a bunch of misfortunes by not banning you. These could range from relevant, like the next few beer shipments "mysteriously" getting damaged during delivery, to completely random gaslighting-esque punishments, such as the bartender's daughter not getting admitted into the local high school. A plethora of plausibly deniable, no-outright-ban social mechanisms existed to make life difficult for people who disagreed with the official narrative, and to encourage people to ostracize the disagreeable. It required only a few well-placed entryists, made sure that ordinary citizens had skin in the game, and was a lot easier to handwave away than the black cars and heavy-handed approach that riled up the opposition in the previous years [3].
[1] https://meanwhileinbudapest.com/2020/09/11/klubradio-going-d...
[2] https://www.bbc.com/news/blogs-china-blog-40627855
[3] https://en.wikipedia.org/wiki/East_German_uprising_of_1953 https://en.wikipedia.org/wiki/Hungarian_Revolution_of_1956 https://en.wikipedia.org/wiki/Prague_Spring