You're reading this wrong, they're not saying that free speech shouldn't be a right but that "free speech is important because it protects free speech" isn't very useful when trying to evaluate whether the government itself ought to also have or not have free speech protections.

Is free speech important solely because it protects you against a malicious government and therefore there's no issue at all with non-government entities censoring others' speech and no reason for the government itself to have it? Or is it important because the marketplace of ideas confers some societal benefit and it would be better if agents of the government were equal participants in that market?

I think you might be reading something that's not there. Asking the question doesn't imply an answer. And it's probably better if people can answer it rigorously rather than just repeat the claim because everyone else does.