If you are thinking about things like earthquake, volcano, flood, hurricane and so on, people will still trust the government for updates and guidance if they don't have a better alternative. There still remains a lot of trust in government. I don't buy the narrative that people are not trusting governments. It's not like Washington D.C. is in flames, politicians are hanging or anything like that. Compliance is at all time highs.
Aside from those, what would be a "real" emergency that cannot be solved without the government? It seems that all "emergencies" are created by governments themselves. That's the point of the article you posted. Governments appear to be fabricating "emergencies" and "issues" in order to justify their existence, precisely because of a lack of major real problems. It's an autoimmune disease.
Fear not the demise of governments, for we already have better coordination mechanisms. They are called Bitcoin and Nostr. We just need to make sure that they are ready in time to replace the existing governments.