In the context of the Constitution, government censorship is the only thing that the United States cares about.

If we valued banning all censorship we'd make laws banning that. We don't: we value private property and free speech instead. Taking the rights of private parties to control what they publish tramples both of those rights. It's not complicated: you have a right to own your 'press' and do whatever you want with it. You don't have a right to someone else's press.

Censorship is free speech?