You can turn these off in the US, although not in some other countries (like Canada). Go to Settings -> Notifications, scroll down past the long list of apps, and then disable (as of this writing) AMBER Alerts, Emergency Alerts, Public Safety Alerts, and Test Alerts.
That said, I live in a part of the country where the government won't be able to tell you that a horrible disaster is coming (earthquake country). If I lived in Tornado Alley or someplace that floods, I'd have mulled over the emergency and public-safety alerts switches longer.
But I don't want to turn it off. We got a useful warning about a nearby fire causing soot (this is in The Netherlands), allowing us to close our windows timely.
That said, I live in a part of the country where the government won't be able to tell you that a horrible disaster is coming (earthquake country). If I lived in Tornado Alley or someplace that floods, I'd have mulled over the emergency and public-safety alerts switches longer.