Market forces and competition should help keep speech free because if a private company doesn't allow x group to use their platform, it is likely a competitor will spring up to capture the orphaned market. We see this play out in reality.
This doesn't really apply in the same way in social media. Social media platforms organically turn into monopolies.
X and Facebook and Reddit and Hackernews and Whatsapp are all social media, sure, but they are not in direct competition. One does not start or stop using Instagram because they use Reddit. Same with Hackernews and X, etc etc. The product is different.
When you ban an ideology or a group from a piece of social media, they do run to competitors, but "competitors" which can never penetrate the market because they don't have the userbase, which is the main incentive of social media.
So far-right people get banned from Twitter and they run to Gab, but Gab and Twitter aren't really competitors because Twitter can't ever penetrate into Gab's market (they banned that market to begin with) and Gab can't penetrate Twitter's market (because Twitter is the more attractive platform to begin with, having more users)
The better product is better because of its userbase. There is no real competition, and as such, no upholding of freedom of speech due to it.
If the private sector is more susceptible to moral policing than the public sector, then (all things being equal) if public services are transferred to the public sector(ie: smaller government) then the attack area increases.
There are two conditions, and one conclusion. If you don't agree that the premises apply, then the argument doesn't really matter and also doesn't apply.