It's less about the absolute goodness of free speech but rather, a problem of the moderator model that you speak of, that the Constitution is explicitly addressing. There are many forms of speech that are unlawful - child pornography, defamation, violation of copyrights, imminent threats, intentional infliction of emotional distress, etc. They're not generally controversial, but they affect and intrude upon the rights of others in clear-cut ways, or have been defined by the courts in a way that there can be such a determination. But if you want some sort of broader, categorical and preemptive prohibition coming from the state you run into the problem we have with policing generally - that even well-intentioned authorities frequently create enormous unforeseen damage down the line, and we just had the president essentially spend a huge amount of time openly trying to coerce private companies into carrying his fringe message with quasi-legal proclamations and in some cases, actually using state coercion in the form of denying fair competition over contracts. HN is a private platform, if you get kicked off here there's very little real consequence. The government makes the stakes instantly higher because without enforcement the laws are more or less just words on paper but the criminal justice system's inequities are well known and well documented enough that merely having state moderation can actually push things in a worse direction real quick. See: the PHilippines for example.
Private platform moderation is in a sense the ideal solution if platforms are actually willing to do it. The Constitution protects their first amendment rights too, and that is the right to decide who can and can't use your platform. The tradeoff is that the state for the most part can't force you to carry messages you don't want to carry, in exchange the state also can't easily force you to act as their auxiliary in enforcing only content that the state likes. It's not really a matter of speech in itself in a philosophical sense but rather, appropriate ways to actually prevent things like violent insurrections or lynchings or agitprop being spread in a world where outside of the few and already prohibited forms there's some room for interpretation, and also, some room for bad faith from either side. It's less about how much free speech has quantifiably benefitted our society - which one can certainly make an argument for - but rather, the consequence of giving reins to a moderator that has the power to literally deny one's liberty and ruin someone's life in an officially sanctioned and prolonged fashion when there's no guarantee that the moderator would be able or willing to act in a way that isn't arbitrary but still effective. Every other platform is built on the basis of consent - as in one joins it at their will and one gets removed from it at the will of the moderators. The law works through coercion. The stakes are quite different.
And speech itself is only the most immediate manifestation of bigger problems in society anyway. The underlying sentiments don't go away, they just become clandestine and fester. It's not something punitive punishment can readily solve. Prohibition didn't work here, the war on drugs is an abject failure, the myriads of exclusionary laws congress passed from the 1880s to the 1940s both failed to actually stop people of different ethnic backgrounds from having relationships and at the same time contributed to a particularly cruel handling of refugees that added to the holocaust death tolls. In more authoritarian countries, China's porn ban, which is actively enforced with sites being taken down constantly, does almost nothing to actually prevent access (nor did it bring the moral salubriousness that it was supposed to bring). Internal passports didn't stop people from seeking work elsewhere and becoming second class citizens. Our own immigration system becomes more disastrous in every possible way as soon as we decided to actively enforce it. The DMCA and CFAA, both with punitive criminal and civil liabilities, have failed to stop piracy or computer intrusion (especially since that part of the CFAA was a response to a pre-WWW Matthew Broderick movie) but did encourage a lot of companies that sell ineffective solutions backed with FUD and hamper effective open disclosure and penetration testing for quite some time. The underlying incentives haven't changed. Banning the symptoms is easy and possibly even politically expedient but represents a bandaid over a gashing bleeding wound. Good speech can make bad speech irrelevant in some cases but it's neither reliable nor address the underlying problems. There's a far right nationalist movement in Germany again. Mere censorship can only go so far.
Unless you can come up with a way to, without resorting to mass coercion, create a system that can fairly act as this moderator and be accepted as fair across the board, it's almost certainly worse, not better, to allow active state interference.The deplatforming case is actually about exercising one (comapny)'s free speech rights, AWS can't violate the 1st amendment rights of Parler. And if they can't find some sketchier but less takedown-happy bulletproof-ish server overseas to host their shit, it's their own fault, they're not entitled for official promotion of their viewpoints. Allowing government regulation of speech will allow that.