Excellent point, but it's important to note that currently the systems private companies use are little better than censorship. We need a non-affiliated govt agency to handle censorship/moderation requests.
You don't have to support.
The government will take your support at gunpoint. This is the crux of the issue.
I'm not on either of those platforms, so they're not shipping me ads. I do what I can to be private, so that their data mining doesn't get me.
I have that choice. Unfortunately if I don't agree with what my government is doing, they'll still take my tax dollars and fight forever wars with them.
Censorship is the moderation of content that may be disturbing or cause painful thoughts or feelings. So a person leaking state secrets on Twitter, and the government asking Twitter to take the tweet down, is not censorship: it's protecting national security, or law enforcement. They're drastically different things being taken down for very different reasons.
You don't need an independent body to handle either type of request because we already have mechanisms for a company to handle both. What people are getting worked up over now is the potential for governments to abuse their legal right to remove illegal content, in order to censor. Since it's the govt doing it, the govt is not going to create an agency just to wave a big flag when it is doing something bad. That would be like creating a "National Agency Of We Don't Trust The Government".