This is an interesting assertion. Many, many people acted responsibly during the pandemic, and in a worst case scenario such as what you described, it's even more likely that a sizable population will gravitate to any source of reliable information.
The government is usually the source of last resort for many, many things. Whether it's as a lender (e.g bailouts) or as a source of information (emergency broadcasts), it's at the scope of the nation state where extreme contingencies exist and must be accounted for. I imagine AM radio is perfect for this precisely for worst-cases, e.g where someone might seek to make a crystal radio, but I'd be out of my depth thinking beyond this.
I actually was neutral on this until I read your comment and thought it through far enough to reply, so thanks for that.