Why wouldn’t they? Nominal proponents of open society in the West were all too happy to engage in censorship during an emergency rather than stand by their principles. What would motivate people to embrace an open society if the nominal proponents don’t?
Which emergency are you referring to? And what censorship methods are you referring to? For example, I think the media choosing not to cover a story immediately when it is being peddled by an unreliable political agent doesn’t qualify as censorship. Even if it turns out to be true.
But since you mentioned not covering a story — we also have the Hunter Biden laptop, which wasn’t merely not covered, but actively censored on social media during an election. (Facebooks Mark Zuckerberg admitted as much.) The whole point of freedom of speech is the censors are notoriously bad at deciding what is “misinformation”, as they were in that case… where they shut down a political story which hurt their preferred candidate but was nonetheless true.