So, yeah. Let's not have governments deciding "truth" and censoring everything else, because governments can be wrong. Even with the best of intent, governments can be wrong. But if they're wrong and they censor what is right, they're going to have a hard time learning that they're wrong.
Worse, if they do learn that they're wrong, they have bureaucratic inertia built up. They're likely to keep censoring the truth for a while after they know it's true, because changing would mean that some bureaucrats have to eat crow.
Even worse, we have plenty of examples of censorship that is not "with the best of intent". It's to preserve the existing power structure. Let's not create the temptation to use our own governments in that way.
Yes, Covid misinformation is a huge problem. No, government censorship is not the answer.
It's always interesting to see how people spin narratives to fit their own biases and preconceived notions, as exemplified by the criticism of vaccines in this context. If the general public was more likely to be thoughtful and considerate, rather than bombastic and dismissive, there would (probably) be fewer such news stories about restricting the spread of misinformation.